How can he maintain his fast in the face of these sins?
Question

How can I maintain my fast in the face of these sins?.
Praise be to Allah.You have done very well to ask this question; it indicates that you are keen to make sure that your acts of worship do not go to waste or be reduced because of these widespread sins. 
We should all remember that the real meaning of fasting is not only giving up food and drink, rather Allah, may He be exalted, has enjoined fasting in order that we may attain piety (taqwa). Hence real fasting means refraining from sin by refraining from it and giving it up; this is the fasting of the heart, not just the fasting of the body. The Sunnah points to what we have said, and it has been discussed and explained by the scholars. 
It was narrated that Abu Hurayrah (may Allah be pleased with him) said: The Messenger of Allah (peace and blessings of Allah be upon him) said: “Whoever does not give up false speech and acting upon it, Allah has no need of his giving up his food and drink.” Narrated by al-Bukhari (1804). And it was narrated that Abu Hurayrah (may Allah be pleased with him) said: The Messenger of Allah (peace and blessings of Allah be upon him) said: “It may be that all a fasting person gets from his fast is hunger and thirst, and it may be that all a person who prays at night gets from his prayer is sleeplessness.” Narrated by Ahmad (8693); classed as saheeh by Ibn Hibbaan (8/257) and by al-Albani in Saheeh al-Targheeb (1/262). 
The Sahaabah and the early generations of this ummah were keen for their fasting to be a purification for their souls as well as their bodies, free from disobedience and sin. 
‘Umar ibn al-Khattaab (may Allah be pleased with him) said: Fasting does not mean abstaining from food and drink only, rather it is also abstaining from lying, falsehood and idle speech. 
Jaabir ibn ‘Abd-Allah al-Ansaari said: When you fast, then let your hearing, sight and tongue fast from lying and sin and stop abusing servants. Be tranquil and dignified on the day of your fast, and do not let the day you do not fast and the day you fast be the same. 
It was narrated that Hafsah bint al-Sireen – who was a scholar of the Taabi’een – said: Fasting is a shield, so long as one does not make holes in it it, and making holes in it means gheebah (backbiting). 
It was narrated from Maymoon ibn Mahraam that the least of fasting is giving up food and drink. 
These reports were quoted by Ibn Hazm in al-Muhalla (4/308). 
So it is no wonder if we learn that some scholars regarded the fast as invalid if a person falls into sin during his fast, even though the correct view is that this does not invalidate the fast, but undoubtedly it detracts from it and goes against the real meaning of fasting. 
Al-Haafiz Ibn Hajar (may Allah have mercy on him) said: 
Backbiting damages the fast. It was narrated from ‘Aa’ishah, and al-Awzaa’i also said this, that backbiting breaks the fast of the fasting person and he has to make up that day. Ibn Hazm went further and said: It is invalidated by every sin that a person commits deliberately, when he is aware that he is fasting, whether it is an action or a word, because of the general meaning of the words “he should not utter obscene speech or behave in an ignorant manner” and because the Prophet (peace and blessings of Allah be upon him) said: “Whoever does not give up false speech and acting upon it, Allah has no need of his giving up his food and drink.” End quote. 
Fath al-Baari (4/104). 
Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allah have mercy on him) said: 
As for the thing from one which must abstain when fasting, perhaps you will be surprised if I tell you that the thing from one which must abstain when fasting is sin. A person must abstain from sin when fasting because this is the primary aim of fasting, because Allah, may He be blessed and exalted, says (interpretation of the meaning): 
“O you who believe! Observing As-Sawm (the fasting) is prescribed for you as it was prescribed for those before you, that you may become Al-Muttaqoon (the pious)”[al-Baqarah 2:183]. 
It is not so that you may become hungry, or so that you may become thirsty, or so that you may refrain from relations with your wife! No; He says “that you may become Al-Muttaqoon (the pious).” This is the primary aim of fasting. The Prophet (peace and blessings of Allah be upon him) affirmed that when he said: “Whoever does not give up false speech and acting upon it and ignorant behaviour, Allah has no need of his giving up his food and drink.” So if a person refrains from disobeying Allah, this is true fasting. As for outward fasting, this is abstaining from things that invalidate the fast and refraining from things that break the fast from dawn until sunset as an act of worship towards Allah, because of the verse in which Allah says (interpretation of the meaning): 
“So now have sexual relations with them and seek that which Allah has ordained for you (offspring), and eat and drink until the white thread (light) of dawn appears to you distinct from the black thread (darkness of night), then complete your Sawm (fast) till the nightfall”[al-Baqarah 2:187].
We call this kind of fasting outward fasting, which is the fasting of the body only. As for the fasting of the heart, which is the primary aim of fasting, this means refraining from disobedience towards Allah, may He be glorified and exalted. 
Based on this, if a person observes the fast outwardly, in the physical sense, but he does not fast in his heart, then his fast is severely deficient, but we do not say that it is invalid, rather we say that it is lacking. Similarly, we say concerning prayer that the aim of prayer is humility before Allah, may He be glorified and exalted, and prayer of the heart comes before prayer of the limbs, but if a person prays physically but not with his heart, not focusing at  all, then his prayer is very deficient, but it is still valid as it appears to be, but is very deficient. Similarly the fast is very deficient if a person does not refrain from disobeying Allah, but it is valid, because acts of worship in this world are to be judged as they appear to be. End quote. 
Liqaa’aat al-Baab il-Maftoohah (116, p. 1). 
Secondly: 
The scholars divided patience into three categories: patience in obeying Allah, patience in refraining from disobeying Him, and patience in accepting the Divine decree. Fasting combines all these kinds of patience.  
Ibn Rajab al-Hanbali (may Allah have mercy on him) said: 
The best kind of patience is fasting, for it combines all three types of patience. It is patience in obeying Allah, may He be glorified and exalted, and it is patience in refraining from disobeying Him, because a person gives up his desires for the sake of Allah even though his self may be longing for them. Hence it says in the saheeh hadeeth that Allah, may He be glorified and exalted, says: “All the deeds of the son of Adam are for him, except fasting. It is for Me and I shall reward for it, because he gives up his desire and his food and drink for My sake.” Fasting also involves patience in accepting the consequences which may result in hunger and thirst for the fasting person. End quote. 
Jaami’ al-‘Uloom wa’l-Hikam (p. 219). 
Whoever manages to fast as Allah has prescribed will attain a great reward from his Lord, may He be blessed and exalted. It is sufficient for him to know that Allah says (interpretation of the meaning): 
“Only those who are patient shall receive their reward in full, without reckoning”[al-Zumar 39:10]
Thirdly: 
In order for the Muslim to protect his fasting from being deficient due to committing sins, he must achieve patience in refraining from sin. One of the scholars said that patience in refraining from sin is greater than the other two types of patience. 
Ibn al-Qayyim (may Allah have mercy on him) said:  
Here there is an issue which people debated about: which type of patience is better – patience in refraining from sin or patience in obeying Allah? One group of people suggested that the former is better, and they said that patience in refraining from sin is the attitude of the siddeeqeen, as some of the salaf said: Good deeds are done by righteous and immoral alike, but no one has the power to refrain from sin except a Siddeeq, and because the motive to commit sin is greater than the motive to stop being obedient, because the motive to commit sin is pleasure, but the motive to stop being obedient is laziness and sloth, and undoubtedly the motive to commit sin is stronger. They said: Sin may be promoted by one's own self, whims and desires, the shaytaan, worldly reasons, a man’s companions, a desire to imitate, and natural inclinations. Any one of these factors may cause a person to commit sin, so how about if they are combined and prevail over the heart? What patience can be stronger than patience in refusing to respond to them? If Allah did not give him patience, he would not be patient by himself.  
This argument, as you can see, is very strong and very clear. End quote. 
Tareeq al-Hijratayn (p. 414). 
Patience in refraining from sin stems from a number of things which we hope you will ponder, for that contains a description of the disease and a prescription of the remedy. 
Ibn al-Qayyim (may Allah have mercy on him) said:  
The principle of patience in refraining from sin is based on a number of things: 
1 – Knowledge of how reprehensible and vile it is, and that Allah has only forbidden it as a protection against its evil, just as a caring father will protect his child from things that will harm him. This reason will make the wise person refrain from it, even if he does not pay attention to the warning of punishment.  
2 – Feeling shy before Allah, may He be glorified. If a person realizes that Allah is watching him and can see him and hear him, he will feel too shy before his Lord to expose himself to His wrath. 
3 – Remembering the blessings He has given you and His kindness towards you. Sins inevitably take away blessings. No person commits a sin but one of the blessings of Allah is taken away because of that sin. If he repents, then it is restored, but if he persists in it, it is not given back to him, and the sins continue to take away blessings until the blessings disappear altogether. Allah says (interpretation of the meaning): 
“Verily, Allah will not change the (good) condition of a people as long as they do not change their state (of goodness) themselves (by committing sins and by being ungrateful and disobedient to Allah)” [al-Ra’d 13:11]
The greatest of blessings is faith, but the sins of zina, stealing, drinking alcohol and robbery take them away and cause them to disappear. One of the salaf said:  I committed a sin and I was deprived of praying qiyaam for a year. Another said: I committed a sin and I was deprived of understanding of the Qur’aan. Concerning such things it was said: 
If you have been blessed then take care of it, for sin takes away blessings. 
To sum up: Sin is a fire that consumes blessings, just as fire consumes wood, Allah forbid that His blessings be lost. 
4 – Fear of Allah and of His punishment. This may be established by believing in His promises and warnings, and by believing in Him, His Books and His Messengers. This is strengthened by means of knowledge and certain faith, and it is weakened if those two things are weakened, Allah says (interpretation of the meaning): 
“It is only those who have knowledge among His slaves that fear Allah”[Faatir 35:28]
One of the salaf said: Fear of Allah is a sign of knowledge and taking Allah’s forgiveness for granted is a sign of ignorance.  
5 – Love of Allah. This is the strongest factor in being patient in refraining from disobeying Him. The one who loves will be obedient to the one whom he loves. The stronger that love grows in his heart, the more his willingness to obey Him and his unwillingness to disobey Him will grow. Sin and disobedience stem from weakness of love. There is a difference between one who is motivated to avoid disobeying his master because of his fear of his whip and punishment, and one who is motivated to avoid that because of his love for his master. 
6 – Nobility and purity of heart. If a person has self-respect and is keen to attain virtue, he will refrain from anything that may lead to doom and dishonour. 
7 – Certain knowledge of the consequences of disobedience and the harm that may  result from it, such as blackening of the face, darkness in the heart, distress, grief, pain, depression, anxiety, lack of focus, weakness in the face of one’s enemy, confusion, sense of abandonment, being overpowered by one’s enemy, failing to benefit from knowledge, forgetting what one has already learned, and sickness that will surely lead to death if it takes hold, because sins deaden the heart.  
To sum up: the awful effects of sin are too many for a person to grasp, and the good effects of obedience are too many for a person to grasp. The best of this world and the Hereafter may be attained by obeying Allah, and the worst of this world and the Hereafter comes from disobeying Him. Concerning some of these effects Allah says (interpretation of the meaning): “Who could ever obey Me and be doomed because of it and who could ever disobey Me and attain blessings because of it?” 
8 – Lack of worldly hope and certainty that he will soon depart this world, and the realization that he is like a traveller who enters a town determined to leave it, or like a rider who rests in the shade of a tree then moves on and leaves it. Because he knows how short his stay will be and how quickly he will move on, he is keen to leave behind anything that may weigh him down or cause him harm and bring no benefit.  He is keen to move on with the best that he has. A person has nothing better than a lack of worldly ambition and nothing more harmful than procrastinating and focusing on worldly ambitions.  
9 – Avoiding excess in his food, drink, clothing, sleeping, and meeting people, because the temptation to commit sin grows stronger if there is any excess in these areas, because that requires an outlet and what is permissible becomes no longer enough and one begins to transgress into haraam areas. One of the most harmful things for a person is idleness and free time, because the soul is never idle; if it is not kept busy with beneficial things it will inevitably occupy itself with harmful things.  
10 – This sums up all the previous things: it is faith that is firmly-rooted in the heart. Patience in refraining from sin depends on strength of faith. The stronger a person’s faith is, the more patient he will be, but if his faith is weak his patience will be weak too. If a person’s heart is filled with the belief that Allah is watching him and can see him, and has forbidden what He has forbidden to him and will be angry with the one who does it and punish him, and if his heart is filled with the belief in the reward and punishment, Paradise and Hell, then he will not fail to act upon this knowledge. Whoever thinks that he can give up sin without firm and deeply-rooted faith is mistaken. If the lamp of faith is strong in the heart it will illuminate all of its corners and shine its light into its depths; that light will then spread throughout his body and he will respond quickly to the promptings of faith, and will obey humbly and willingly, with no resentment. Rather he will rejoice in this call when it comes, just as a man rejoices in the call of his beloved who calls him to show him kindness and honour him, so he is waiting for his call all the time. Allah bestows His mercy upon whomsoever He will ... End quote. 
Tareeq al-Hijratayn (p. 408-414). 
What is required of the Muslim is to understand what Allah really wants from his fasting, and to understand what pushes him to commit sin, so that he may keep away from it and shun it and hate it. What we have quoted from Ibn al-Qayyim explains this in the best way. 
See also the answer to question no. 12468. 
And Allah knows best.