Why do people die of old age?

When someone dies and the cause of death is listed as “natural causes”, i.e. they died of old age, what is the actual cause of death? I am assuming that there is a single point of failure and there is usually no need to determine what exactly has caused the person to die but my question is why did that particular organ stop doing it’s job?

In general our bodies seem to be quite adept at repairing themselves so why can’t they repair the damage caused by time?