Should I Do Wudu for Every Sunnah Prayer?
Question

Is performing Wudu for every supererogatory (supererogatory) prayer recommended as Bilal ibn Rabah (may Allah be pleased with him) used to do?
Praise be to Allah.Did Bilal ibn Rabah do Wudu for very Sunnah prayer?
Al-Bukhari (1149) and Muslim (2458) narrated from Abu Hurayrah (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) said to Bilal (may Allah be pleased with him), at the time of Fajr prayer: “O Bilal, tell me of a deed that you did in Islam, for which you most hope to earn reward, for I heard the sound of your sandals in front of me in Paradise.” Bilal (may Allah be pleased with him) said: I have not done any deed in Islam for which I hope to earn reward more than the fact that I do not purify myself fully (Wudu) at some time of the night or day, but I pray as much as Allah wills I should pray with that purification. 
At-Tirmidhi (3689) narrated that Bilal (may Allah be pleased with him) said: I never gave the Adhan but I prayed two Rak`ahs, and I never invalidated my Wudu but I did Wudu immediately and thought that I owed it to Allah to pray two Rak`ahs. (Classed as authentic by Shaykh Al-Albani (may Allah have mercy on him) in Sahih Sunan At-Tirmidhi) 
The Hadith of Bilal (may Allah be pleased with him) indicates that it is recommended to persist in doing Wudu, and that it is recommended to offer a prayer immediately after doing Wudu. 
There is nothing in the Hadith to indicate that it is recommended to do Wudu for every supererogatory prayer. 
An-Nawawi (may Allah have mercy on him) said: 
This indicates that it is recommended to pray following Wudu, that doing so is Sunnah and that it is permissible to do so at times when offering (unspecified supererogatory) prayers is disallowed: at sunrise, when the sun is at its zenith, at sunset, and after Fajr and `Asr prayers, because it is a supererogatory prayer that is done for a specific reason. This is our view.” (Sharh Muslim by An-Nawawi, 8/13) 
Ibn Hajar (may Allah have mercy on him) said: 
“This Hadith indicates that it is recommended to keep oneself in a state of purity.” (Fath Al-Bari, 3/35) 
Is it recommended to renew Wudu?
The scholars (may Allah have mercy on them) stated: Renewing Wudu is only recommended for one who prayed after doing the first Wudu. 
An-Nawawi (may Allah have mercy on him) said: 
“Our companions unanimously agreed that it is recommended to renew Wudu , which is when a person had Wudu, then does Wudu again without having invalidated his Wudu. 
When is it recommended? There are five views concerning that, the soundest of which is if he offered a prayer, obligatory or supererogatory, with the first Wudu (then it is recommended to do Wudu for another prayer).” (Al-Majmu`, 1/495) 
Shaykh Al-Islam Ibn Taymiyah (may Allah have mercy on him) said in Majmu` Al-Fatawa (21/376): 
“Rather the jurists’ discussion has to do with the one who prayed with the first Wudu: is it recommended for him to renew his Wudu?” 
With regard to one who did not pray with the first Wudu, it is not recommended for him to renew Wudu . Rather renewing Wudu in this case is a Bid‘ah (innovation) and is contrary to the Sunnah of the Messenger of Allah (blessings and peace of Allah be upon him) and the way of the Muslims both during his lifetime and after his death, until the present time.”
When is it not recommended to renew Wudu?
An exception is made to it being recommended to renew Wudu if one of the two prayers was connected to the other, such as the regular Sunnah prayers that are connected to obligatory prayers, or Tarawih followed by Witr, or if the two prayers are joined together, as in the case of one who joins Maghrib and ‘Isha’ together. In such cases it is not recommended to renew Wudu, because there is no report of the Prophet (blessings and peace of Allah be upon him) doing that.
Shaykh Al-Islam Ibn Taymiyah (may Allah have mercy on him) said: 
“It is proven via Mutawatir reports that on the day of `Arafah the Prophet (blessings and peace of Allah be upon him) led the Muslims in praying Thuhr and ‘Asr, joining the two prayers together, and thousands prayed behind him whose numbers are known only to Allah. When he (blessings and peace of Allah be upon him) said the Tasleem at the end of Thuhr, he led them in praying ‘Asr; neither he nor anyone else repeated his Wudu, nor did he instruct anyone to repeat his Wudu, and no one transmitted any report to that effect. This indicates that renewing Wudu is not recommended in all cases. 
Sometimes he would offer an obligatory prayer and then a supererogatory prayer, and sometimes he would offer a supererogatory prayer and then an obligatory prayer, and sometimes he would offer an obligatory prayer then another obligatory prayer, all of that with one Wudu. 
Similarly, the Muslims would pray behind him at night in Ramadan with one Wudu, on numerous occasions. 
The Muslims at his time would do Wudu, then they would pray so long as they did not invalidate their Wudu, as is mentioned in authentic Hadiths. There is no report from him – either with an authentic or inauthentic Isnad (chain of narration) – to indicate that he instructed them to do Wudu for every prayer. Saying that it is recommended to do so requires proof.” (Majmu` Al-Fatawa, 21/371-372)
And Allah knows best.