Is the prayer of one who has a pilonidal sinus from which a small amount of blood comes out onto his trousers valid?

Blood exiting from inside the anus (rectum) invalidates ablution (wudu') according to the soundest opinion. If it is continuous, such that you do not find a time to pray with complete purity, then you perform ablution for each prayer, and what exits does not harm you. However, if you find a time for complete purity, then you must pray within that time; otherwise, your prayer is not valid. As for blood that does not exit from inside the anus, it does not invalidate ablution, but it is an impurity that must be cleansed and guarded against. And you must repeat the missed prayers if you failed to meet their conditions.