How Long Can You Wipe Over Socks?
Question

I am 60 years old. I am suffering from an illness in my back that makes it hard for me to bend over and wash my feet during Wudu (ablution) . Is it permissible for me to wipe on my socks for a long period of time?.
Praise be to Allah.The Time Limit for Wiping Over Socks
The authentic Sunnah indicates that wiping over the socks is limited to a specific time period, which is one day and one night for the non-traveller, and three days and nights for the traveller.
Muslim (276) narrated that Shurayh ibn Hani’ (may Allah have mercy on him) said: I came to `A’ishah and asked her about wiping over the Khuffayn. She said: You should go to (`Ali) ibn Abu Talib and ask him, for he used to travel with the Messenger of Allah (peace and blessings of Allah be upon him). So we asked him and he said: The Messenger of Allah (peace and blessings of Allah be upon him) set a limit of three days and nights for the traveller, and one day and night for one who is not travelling.
At-Tirmidhi (95), Abu Dawud (157) and Ibn Majah (553) narrated from Khuzaymah ibn Thabit (may Allah be pleased with him) that the Prophet (peace and blessings of Allah be upon him) was asked about wiping over the Khuffayn and he said: “For the traveller it is three (days) and for the non-traveller it is one day.” (Classed as authentic by Al-Albani in Sahih At-Tirmidhi)
When Does the Time Period for Wiping over Socks Begin?
The most correct scholarly view is that the period for wiping over the socks begins from the first time one wipes over them after breaking Wudu, not from the time of putting them on. So if a person does Wudu for Fajr prayer, and puts on socks, then he breaks his Wudu at nine a.m. and does not do Wudu, then he does Wudu at twelve o’clock, then the period begins from twelve, and lasts for one day and one night, i.e., twenty-four hours.
An-Nawawi (may Allah have mercy on him) said: Al-Awza`i and Abu Thawr said: The period begins from when he wipes over his socks after breaking Wudu. This was narrated from Ahmad and Dawud, and it is the favoured view and the most likely to be correct based on evidence. It was the view favoured by Ibn Al-Mundhir, and something similar was narrated from `Umar ibn Al-Khattab (may Allah be pleased with him). (End quote from Al-Majmu`, 1/512)
What to do When the Wiping Period Ends?
Based on that, you should follow the period for wiping over the socks, and when it ends it is not permissible to wipe over the socks, until you take them off then put them on after purifying yourself fully. But the end of the period does not mean that Wudu becomes invalid, according to the more correct view, so if the period ends and you are still in a state of purity, it is permissible for you to pray with this purity until it is broken.
Dealing with Difficulties in Washing Feet
What you mention about it being difficult to wash the feet can be overcome by sitting on a chair and the like, or pouring water over the feet without bending down to wash them.
An-Nawawi (may Allah have mercy on him) said: Our view is that rubbing the limbs when doing Ghusl and Wudu is Sunnah but is not obligatory. If a person pours water over it and does not wipe it with his hands, or immerses himself in a lot of water, that is sufficient for his Wudu or Ghusl. This is the view of all the scholars except for Malik and Al-Muzani, who stipulated that in order for Ghusl and Wudu to be valid. (End quote from Al-Majmu`, 2/214)
We ask Allah to heal you and make you well.
And Allah knows best.