We all know that in 1974 phlebitis forced Richard Nixon to become the first president of the US to resign for health reasons. Suppose he had been healthier, though?
(Just because Nixon eventually recovered, you hear all sorts of unsubstantiated stories that there was some other "real" cause of the resignation, like some scandal to which Nixon was supposedly associated. I think we can dismiss all such stories as conspiracy theory nuttiness. If there were such a scandal, surely it would have been uncovered by now.)