Is it better and closer to the Sunnah of the Prophet, may Allah’s prayers and peace be upon him, to renew ablution for every prayer (such as the Asr prayer after waiting for it in the mosque, or the Dhuhr prayer after the Duha prayer), or is it sufficient to rely on the first ablution as long as it has not been invalidated?

It is recommended to renew ablution for anyone who has prayed with the first ablution, even if it was a supererogatory prayer. This is the soundest opinion according to the Shafi'is. However, if a person has not prayed anything with their first ablution, then it is not recommended for them to renew it; rather, it is considered an innovation (bid'ah) contrary to the Sunnah, as stated by Sheikh al-Islam. Al-Nawawi mentioned that the soundest of the Shafi'i opinions is the recommendation of renewing ablution for anyone who has prayed with the first ablution, whether it was an obligatory or a supererogatory prayer. Sheikh Ibn 'Uthaymin said that renewing ablution is sunnah if one has prayed with the previous ablution.