If you do not take care of yourself, eat right, and exercise, of course your health would deteriorate.
Your question is true in some ways. It is part of the normal aging process and in your cells, there is this thing called DNA and it continually replicates itself. However, if it reaches a certain point (Hayflick Limit), your cells would stop replicating and start senescence. This would result in aging and degenerative diseases would develop.
Interesting studies are now being done to extend the tip of the DNA called telomeres. These telomeres are the one being used up and shortened everytime the cell replicates and without it, your cell becomes unprotected. Think of it as the tip of the shoelace. Without the plastic tip, the shoelace threads will become haywire. If there is a way to increase the telomeres without developing cancer cells, then there is a possibility of immortality. :)