I’m be theory about Henry is that he suffered from Kell Syndrome. People who have it are affected in various ways, including psychotic episodes (which he had) and the inability to have more than one child with any partner. The sex doesn’t matter - sufferers can produce male or female babies, but after the first one maternal antibodies attack foetuses in utero. Catherine had Mary, so subsequent babies died or were miscarried. It was the same with Anne - after Elizabeth she couldn’t carry to term. Jane had Edward. She died soon afterwards, but would not have produced any more children if Henry did have Kell blood.
It’s an interesting theory, but is still unproven beyond doubt. There is evidence that at least one of Henry’s ancestors had the syndrome, which is hereditary, however, so it is a plausible hypothesis, and explains why he went from a fit, rational young man to an obese monster in older age - a situation that is often thought to be the result of a fall from a horse.
