It's been addressed a million times, but I'll give it another go...
We live longer, on average, today than we did a long time ago for several reasons. If you look at statistics of people living in primitive conditions, there are several things that are very different from our lives in terms of cause of death. Infant mortality is very high, WAY higher than in modern societies with hospitals, etc. If you look at life expectancy for people who make it through early childhood, the numbers get much higher, I think several decades better. The second thing is violence--murder rates tend to be way higher in primitive societies, especially among younger males. If you control for violent death, the numbers again improve, especially for men. Finally, many people died from acute problems, anything from being attacked by an animal and bleeding to death, getting cut and dying from a simple infection, or breaking a leg when far from home and not being able to move, and starving to death or being eaten. Far fewer people die from that sort of thing today because 1) the most dangerous thing most of do regularly is get in our cars and 2) we have a much higher survival rate from accidents and serious injuries because of modern medicine and 3) modern medicine also prevents minor infections from spreading and killing us in most cases.
If you control for all of these factors, you actually get a lifespan that is not much different than today's, with those who were lucky enough to survive the perils of primitive life routinely living into their 70s and 80s, with a major difference: those who do make it that long living in primitive conditions are healthier on average than their agemates in modern society. The majority of people that age in our society are quite ill and take several powerful medications just to stay alive. Many of them are unable to walk. This is much rarer in primitive societies.
You may not know that life expectancy also took a major dip at the advent of agriculture, and has only reattained its former status with the advent of modern hygiene and medicine.
Sorry I can't dig around for citations for all of this at the moment, don't have time right now.