There have been suggestions of syphilis in the past, but he does not seem to have had that disease ( which in his day was quite deadly and fast). There is a new theory that he was carrying a genetic disease, the Kell Antigen via his grandmother Jacquetta Woodville. This would have created an antibody reaction in women he'd impregnated, causing them to miscarry. There's also some exploration of the possibility that he had another disease, McLeod Syndrome, that eventually made him psychotic and murderous.

It's all very interesting, but of course there are plenty of other examples of kings or rulers unable to produce a male heir, and of kings or rulers very ready to kill people, and they did not all seem to need a genetic disease to do any of this. It seems dubious Henry's body will be exhumed for DNA testing to settle the question.