Is it permissible for a woman who suffers from menorrhagia and irregular menstruation to pray if her menstrual period exceeds 10 or 15 days?

There is no minimum or maximum limit for menstruation in terms of days. So, whenever menstruation occurs, its rulings are established, and whenever purity is achieved, they cease. This is because Allah made the ultimate limit for prohibition (of certain acts) to be purity, not a fixed number of days, and this is the correct view. Therefore, any blood a woman sees that is known among women to be menstrual blood is indeed menstrual blood, without being tied to a specific time period. This is unless the blood is continuous and never stops, or stops for only a short period in the month, in which case it is considered blood of istihadah (non-menstrual vaginal bleeding). A woman is not permitted to pray until her menstrual period ends and she performs ghusl (ritual bath) after menstruation. The cessation of blood is known by one of two signs: the emission of the white discharge (al-qassah al-baida'), or complete dryness from blood.