One of our friend's mother had something like this due to a stroke medication, Teclid, which caused her to have transfusions for over a month. The Teclid took a long time to leave her system. Needless to say, like many pet owners feel, he is our baby. I would be most concerned about a bleeding disorder such as exposure to rat or mouse containing an anti-coagulant in this situation. If this hasn't been ruled out, it would be worth asking your vet about.
Liver disease can lead to problems with blood clotting.
There are some platelet disorders that affect cats, too. In dogs, heartworm disease can lead to coagulation disorders but I do not know if this is seen in cats with heartworms and that seems unlikely in your cat's case, anyway. Auto-immune disease is certainly possible, too. I think your vets probably considered the above possibilities but it doesn't hurt to ask. I wish I could help more.