Some cells in your body do keep regrowing and replace old ones e.g the skin or tissues in the gut.
However some cells cannot be replaced, like nerve tissue for example.
If, in the case of a stroke, where part of the brain (an organ composed of many nerves) no longer has blood supply, and dies, the nerves in that area will never re grow, (even if blood suppy if restored) so you loose the action of that part of the brain.
If its an important area of the brain then you may die; or you may just loose a specific ability (movement, feeling e.t.c.)
Also to consider life span, one must consider organs and how well they work.
The heart (another organ whos cells (myocytes) do not regenerate) over a period of time becomes less elastic, therfore each passing beat becomes harder, and may result in heart failure, or a host of other things (like high blood pressure) before this, reducing overall life span.
The lungs over a period of time collect may different pollutants and so do their job less efficiently.
Eventually a person may start to have breathing difficulties, leading to a host of problems, which can lower a persons life span also.
Cancer causing agents, or carcinogens, like cigarette smoke, once deposited can not only affect the lungs, but can cause untold problems all over the body.
Small cell carcinoma for example (which has a high mortality rate) can spread all over the body in it's end stages. It is primarily caused by cigarette smoke inhalation.
Obviously, genetic, lifestyle, and cultural factors will also affect the way a persons body works, and how well it's cells renew, but in general, a persons ability to renew his or her cells is generally goverened by how well each of the bodys systems (respiratory, digestive, nervous e.t.c.) are working, and how well they can keep work in sync.
Overall this will affect how long a persons body will