With proper manse building, which is quite easy to do if you are an elder celestial exalted, it's quite easy to make a hidden, protected by a small army of second circle demons (or equivalent in power), indestructible fortress. It only goes off from there.
This subject was being discussed some time ago in rpg.net, and if I remember right, one of the writers (I think it was Stephnis, but don't quote me on that), commented that the way he saw, Celestial Exalted were caught by surprise by the fact they could in fact die from old age. After the first few died, they quickly developed ways to prevent this from happening again. After that, the solars and lunars just died from the usual, violent, ways.