The first Vasa King is just a generation ahead of Henry, and he had a Great Grandmother with Bourbon "titles" ~ so reciprocity could have brought Henry's Great Grandfather a clear blue eyed platinum blond beauty in the deal, and WHAMMO ~ indeterminate infertility.
I’m not too much into his history but how much inbreeding was going on then? Like the Tsar’s of Russia? Hemophilia in there perhaps?