What condition(s) can cause a wound not to heal/clot?

My grandmother has an open (small) wound on her thumb that has been bleeding for about 2 weeks now. She does not know how the skin opened. She went to the doctor & they used a cauterizer to close it, wrapped it with a bandage, & gave her antibiotics. It has been a week, & it reopened and started bleeding again. I feel like they should have done some blood tests it seems like it could be an indication of something serious. They offered no theories as to how it may have opened or why it isn't clotting & healing properly.