We used to say this was because rich people took better care of themselves and smoked less, wore seatbelts, got vaccinated, had dental care, bettery bypass surgery, better breast cancer care, etc.
Then, a few years ago, a meme developed that the gap was due largely to power relationships. There was something about being on top that made one live longer (presumably this would be true of other social animals). The statisticians claimed that they'd controlled for the effects of smoking, seat belts, etc.
Now, smoking is back :
Smoking is to blame for half of the difference in male death rates between men in the top and bottom social classes, say international researchers...Half is quite a bit considering that researchers previously thought they'd accounted for the effects of smoking on mortality gaps.
We've seen this many times in healthcare research over the past decades -- case control research is essential and suggestive, but caution is always indicated.
We can't randomize infants to being rich or poor, or switch thousands of accountants and CEOs, so there's no alternative to population research. The results become more persuasive when reinforced by other lines of inquiry . So if the power=health meme is reinforced by animal studies where one can randomize status it becomes stronger, but smoking is a powerfully proven source of mortality.
Occam's razor favors smoking as the simplest explanation for mortality differences, and researchers know that, so for me this is really a story about how hard it is to draw strong conclusions from population studies.
The battle will go on, and power relationships may indeed be more important as smoking decreases, because we need data to guide policy. Is it better to put effort into immunization adherence, smoking bans, breast cancer screening or liver transplants ?
 Science is about consistent and reinforcing models, each supported by variable amoungs of testable predictions. Where tests are less rigorous, we rely more on integration with other parts of the knowledge model.
 The slimeballs haven't given up yet, btw.
 The transplant bit was a joke. To date reducing the rich/poor mortality gap has seemed either relatively inexpensive (seatbelt laws, immunization, smoking bans) or impossible (substance abuse, power relationships). If things like expensive biosubstances, transplants, or stem cell therapies become more important the social strains will be significant.