Does the prayer of one from whom madhy (prostatic fluid) is discharged only during prayer—when thinking about something—become invalidated, without him feeling its discharge until after he has finished the prayer, and without it being discharged at other times?

It appears that what is discharged is not madhy (pre-seminal fluid) but rather normal vaginal secretions. If this discharge is constant during every prayer, such that there is no time for prayer without it, then the questioner's ruling is that of a person afflicted with perpetual impurity (sahib al-salas). She should perform ablution (wudu') for prayer after its time has begun and pray the obligatory and supererogatory prayers with that ablution. She should also ignore and disregard any whispers of doubt (waswas).