[meijer]

Some animals age very, very little: https://en.wikipedia.org/wiki/Negligible_senescence

Among them the Naked Mole Rat, a mammal.

So it looks like evolution can do it. But it usually doesn't.

[joak]

In some animals old age has a reproductive advantage. As for turtles and some fishes: Old age => Bigger => less predators + more eggs

For these species most of the new born are babies of very old females.