What is the ruling on one who frequently experiences Madhy (pre-seminal fluid discharge) for hours and finds extreme difficulty in purifying himself for prayer? Does he need to repeat the prayer if he finds some Madhy after finishing it?

There is no need to stay long in the bathroom and squeeze the penis, nor to be overly anxious. Your situation is one of two things: 1. If madhy (pre-seminal fluid) does not exit continuously and you find enough time for wudu' and prayer, then you must wait until its exit stops, then perform istinja' (washing private parts), wudu', and pray, even if you miss congregational prayer. Squeezing the penis is an innovation and may cause incontinence, and staying in the restroom longer than necessary is blameworthy. 2. If madhy continues to exit such that you do not find enough time for wudu' and prayer, then perform istinja' and wudu' after the prayer time begins, and whatever exits during prayer will not harm you, similar to those with excuses. Placing a wet tissue is not beneficial and increases the spread of impurity.

If the continuous exit of madhy is due to what you mentioned and not for a medical reason, then distance yourself from the causes and avoid causing its exit after the prayer time begins. If time is short, it is obligatory to refrain from everything that conflicts with prayer.