Does wiping over the leather socks need to be repeated with every new state of impurity within the wiping period, or is the first wipe sufficient?

If a Muslim wears his leather socks (khuff) while in a state of ritual purity, he is permitted to wipe over them for one day and one night if he is a resident, and for three days and three nights if he is a traveler. Each time he performs ablution (wudu'), he must either remove his leather socks and wash his feet, or wipe over the leather socks as long as the period allowing this concession (rukhsah) is still valid. It is not permissible to abandon wiping based on a previous wiping, because wiping over the leather socks takes the place of washing the feet, and it is obligatory with every ablution; otherwise, the ablution would not be valid.