Because, says a paper published through the National Bureau of Economic Research, nursing homes have an easier time hiring minimum-wage nursing assistants. At least that's part of the reason. (People also drive less during recessions, so the risk and incidence of vehicular death goes down.)

Robin Hanson explains:

It seems that the puzzle of why death rates rise in good economic times is nearly solved. There’s an effect of increased driving deaths from increased driving, but the main effect is that in good times nursing homes have to compete more for minimum wage nursing assistants. Apparently a one percentage point cut in the unemployment rate leads to three percent fewer nursing assistants, which increases the national death rate by a half percent (which cuts about three weeks of life per person):