I'm going to take a slightly different perspective than Zaralynda - in breeding out many of the issues that cause pets/working animals to die younger, and in providing animals with better care, we've effectively run into the same "wall" that is happening with human longevity.
It looks like there is a built-in genetic "fuse" that determines the maximum lifespan of a given animal. That hasn't changed - in humans, the limit appears to be in the range of 110 - 120 years, but the average lifespan is shorter because of disease, accidents and so forth.
What I think is happening is that as we improve the level of care we give our pets and companion animals, their lifespan gets closer to their genetic maximum - which is something research doesn't understand yet, but it's being worked on (Google longevity research... There's some very interesting things going on there, and some that I think is pretty crackpot).
In my lifetime, the "typical" age when a pet cat would die has gone from 12-14 range to the 16-18 range, and 19-20 isn't rare anymore (and I'm not that old). Large dogs have gone from when a 10 year old big dog was rare and amazing to 10 for a big dog being commonplace.