What is incumbent upon one who performed ablution and put on his socks at Dhuhr time, then wiped over them at Asr time on the same day, and on the following day forgot and wiped over the socks at Maghrib and Isha after the period for wiping had expired, then remembered this on the day after that; does he have to repeat the prayers he performed or not?

The duration of wiping for a resident is one day and one night, and it begins from the time the state of ritual impurity (hadath (definition)) ends. So, if a person performs ablution (wudu') and remains in that state, then experiences hadath, he may wipe for one day and one night starting from the time of the hadath. Any prayers performed thereafter without a complete ablution that includes washing the feet must be repeated.