Answered by Shaykh Faraz Rabbani
What does a person do if he is bleeding and the bleeding isn’t stopping and the time for the prayer is running out or the time for jamah has come?
In the Name of Allah, Most Compassionate, Most Merciful,
Bleeding (such that the blood flows past its point of exit) breaks wudu.
In the case you mention, the person would first have to do their best to stop the bleeding. If the blood still does not stop before the end of the time, then they would have to pray anyways. Then, we look at the pray time after that one: if the blood continues to flow for the whole time without stopping long enough to do a minimum wudu and prayer, then they have a chronic excuse and that prayer is valid. However, if the blood does not continue to flow throughout the second time in this manner, then that prayer is legally invalid, and would have to be repeated (before the current prayer) [As explained by Allama al-Tahtawi in his Hashiyat Maraqi al-Falah].