German statistics referred in Demografische Forschung 2008/3 gives a very strange set of information on marital status and life expectancy: Divorced men live on average 9.3 years less, women 9.8 years less. (This clashes with American research I have read but not bookmarked, claiming that divorced women live longer than married women. Is the culture really that much different, or have I been misled?) Anyway, the real shocker: Unwed men suffer no such "death penalty" for their lack of family values. This is almost certainly wrong, though I can't say how. A man who does not marry is almost certainly sick in body or soul, if not both, unless he happens to be a monk. Perhaps the monks live so incredibly long that they offset the rest. Huh. More research is needed.
But it does make sense for women to ditch men who become chronically ill. Such men will earn less money, but also tend to turn surly and have special needs. Besides, females of virtually all vertebrate species will find unhealthy males sexually unattractive. Humans are, with few exceptions, vertebrates.
Rather than divorce leading to sickness, then, the most likely conclusion is that sickness leads to divorce. Not quite the same thing.