It has long been noted that varies species live wildly varying lengths of time. Tiny flies might last a day, and giant tortoises can live, literally, more than 150 years. What determines this phenomenon is not exactly known, even though there are many theories.
There are, however theories of aging and decline that are starting to converge around certain central ideas. One of those ideas is that aging occurs on a cellular level, and another idea is that aging is the breakdown of the repair mechanisms of the body, and a third very old idea is that natural selection only cares about propagation of the species and cares little about the fate of any individual of that species past the age of fertility.
And so, if you put these three ideas together, you can make this statement: “Your cellular repair mechanisms work fine and are programmed to function until you pass the nominal age of reproduction and then the body is not programmed to maintain the same rate of repair. Cellular damage accumulates, aging is the result, and system failure follows.”
This would explain why there are no immortal species. That would be a very heavy lift for nature and it serves no evolutionary purpose. The birth, reproduce, decline, and death cycle works well and nature will not fix it. Extending the cycle out for many more years is something that we care about, mostly for ourselves, and so we will have to figure out how to make the human repair cycle work better and for longer. When the problem of aging is reduced to the matter of maintaining the repair cycle, it becomes a much easier to understand and one day solve problem. Aubrey de Gray sums this point up nicely at minute 20 of this Ted Talk from way back in 2006. The whole talk is worthwhile, but he answers the question directly at minute 20.