Hi: Bleeding continuously to the point that your father cannot work is surely a concern.
It is not necessarily Leukemia, but if you think your father knows what is wrong then ask him to be honest with you. If he does not really know the problem, then take him to a doctor for a full exam.
I do have Leukemia, and I do not experience nose bleeds. I bruise very easily, and have other problems. I am however on medication for it.
I pray your father does well, and gets the care he needs.
Is his nose dry- is he using saline spray several times a day?
I guess- just rule out the obvious first.
Is he on a blood thinner? Coumadin? Any medication that could make you bleed easier?
Has he lost weight?