What is the legal ruling regarding prayer and purification for someone who suffers from pelvic congestion syndrome, which causes severe and continuous vaginal discharge and gas, preventing her from maintaining her ablution? Is she required to renew her ablution with every prayer, or is she treated like a person with a chronic excuse?

If your discharge reaches the level of سلس ( سلس البول: urinary incontinence, but here refers to continuous discharge), you should perform Wudu' for each prayer after its time has begun, according to the majority of scholars. If you find extreme difficulty, it is permissible to adopt the view of the Malikis, which states that continuous (or perpetual) impurity does not nullify Wudu'. So, if you perform Wudu' for Dhuhr, you may pray Asr with the same Wudu', and it is only invalidated by ordinary excretions.