What is coming off is the outer horn and leaving the live core behind. That will continue to grow and eventually will be covered in outer horn again although it will never match or catch up with the other side.
One good thing to use to stop the bleeding is cobwebs, which act like platelets and gives a matrix for clotting. Someone was telling me yesterday that they had seen shepherds stuff cobwebs inside shearing cuts as a flexible dressing. (dentists use a similar manufactured product to stop tooth sockets bleeding) For the broken horn, just lay as many cobwebs as you can find in your barn (clean is better but it doesn't seem to matter if they are dusty) over the raw stump. As with any head wound, the stump will appear to bleed profusely but the amount of blood lost is not too great. Far more alarming is when the core comes off too so there is a hole in the skull and a major artery is torn - then you need to find the bleeding point and pinch the artery and hold it for a minimum of 5 minutes, then dress the hole.
As for the cause, I would be looking at something mechanical rather than a deficiency. Jacobs love sticking their heads through Rylock fencing and the horns tend to break or come off completely when they pull their heads back. Another cause could be fighting between young males.