Many theories, but the most compelling to me boils down to it not mattering to the processes of evolution
In the harsh reality of life, very few creatures live to see old age. So long as a creature lives long enough to pass its genes on to the next generation, its all good to go. Its probably going to be eaten before it turns grey anyways.
This would make aging a problem that didn't matter if it was fixed or not. Until humans recently (Recent in evolutionary terms that is) started en masse bypassing all the millions of things that made us die young, we didn't even have particular reason to care.
Even though the body has the ability to replicate cells and heal itself the body still ages and gets older. As the body ages it starts to slow down and the cell replication and natural healing slows down too. Over 70 or more years that cell replication and healing has slowed to a crawl making it much harder for the body to continue. This is a natural thing and sooner or later the body stops replicating cells and healing itself to the point it expires.
One thing I find interesting, is that a few creatures partially buck this trend.
Lifespan is typically correlated with body mass, with larger creatures generally living longer.
But there are exceptions. Certain tortoises for instance are the obvious ones, able to exceed the 200 year mark.
Some bats are also remarkable, Vesper bats in particular get up to over 40 years, while sporting a body mass typically associated with only 2-3 years of life.
The genes of these animals could prove very useful in the pursuit of longevity.
Daishain,
Is this due to their DNA or due to a slow heartbeat? I've heard that at least some of reasons some live longer than others, whether human compared to human or species compared to species, has to do with heartbeats and the faster a heart beats the less years it will live.