Is it necessary to ensure that all madhy has exited before prayer, or to wash it off then go to pray, knowing that this causes some prayers to be missed and leads to a cycle of doubt and repeating prayers?

Wadi is a thick, white fluid that exits after urination. Madhi is a thin, white fluid that exits when desire is aroused. Both invalidate ablution (wudu) but do not necessitate a full ritual bath (ghusl). Rather, one must perform wudu and wash the penis from both.

If something exits after relieving oneself, one must wait until it stops, then perform istinja (washing the private parts) and wudu. There is no harm if you miss congregational prayer. One must be cautious of obsessive doubts (waswasa). If you are certain that something has exited, you must wash it and repeat wudu; otherwise, do not pay attention to the doubt.