Must a woman with continuous istihadah perform ablution and purification for each make-up prayer she performs?

Summary

Missed prayers, whether left intentionally or due to a valid excuse, must be made up as far as one is able, with no difference between a person in constant hadath and a healthy person. According to the final position of the Shafi‘i school, the ablution of a person in constant hadath is valid for only one obligatory, make-up or vowed prayer, along with any number of voluntary prayers. If the prayer debt is large and repeated purification is difficult, the lighter Hanafi view may be followed. Under that view, one purifies after the prayer time begins and a single ablution serves for obligatory, make-up, vowed and voluntary prayers within that time, provided nothing else invalidates it.

Written in our own words from the original fatwa — check the source before acting on it.