This one is easy. First of all, evolution only cares about the species as a whole, so the survival of an individual, especially after they've produced their offspring, doesn't matter much. Second, in the wild, animals will be killed by predators much more quickly than they'd die of old age, so all the mutations that only manifest negatively in older age have never had a chance to be selected against.

Besides, the whole premise of evolution is that older generations die.

(disclaimer: I'm a software developer, not a biologist, but I'm fascinated by biology)