What is the ruling on the discharge that comes out of a woman without cause and requires wiping with a tissue to become visible? Does it necessitate repeating the prayer?

These secretions are the vaginal fluids of a woman, which are pure but invalidate wudu'. There is no need to investigate their discharge, as the default is that they have not exited. If you are certain they have exited, repeat wudu'. If you find them after prayer and doubt when they exited, attribute their exit to after the prayer. If they are continuously discharged such that you cannot find time for purification and prayer, then your ruling is that of one afflicted with incontinence: perform wudu' after the time for prayer begins and pray as much as you wish until the time for prayer ends.