Is ablution required before every prayer for one who bleeds from acne, by analogy with one who suffers from urinary incontinence or continuous flatulence, or is it sufficient to perform ablution before the time of prayer and wash off the flowing blood?

The emission of blood from the face does not invalidate ablution, according to the more preponderant opinion of scholars. Therefore, the ruling of the excusable person (sahib al-salas) does not apply to you, and it is permissible for you to perform ablution before or after the prayer time begins.

If the bleeding stops, wait for it to cease, as long as the prayer time has not exited, then wash it and pray. If the bleeding is continuous and does not stop, then you should perform the prayer at its appointed time in your current state, as Umar ibn al-Khattab, may Allah be pleased with him, did.

As for the small amount of blood that is pardoned, some scholars have defined it as the area of a "Baghli dirham," while others have defined it as what is conventionally considered a small amount among people.