Exactly what does the game do when you try to unstable your pet? How long did you leave your pet stabled? It sounds like it was a long time, based on your pet's age.
It's likely that your pet would be dead if you were able to successfully unstable him, since they don't live that long under normal circumstances. The game's instructions say, "If you stable your pet for an extended vacation, don't be surprised if you get him back and he is very old and dies soon."
You might just need to let that pet go and adopt another pet.
_________________________
Barbara
Unicorn
Last Day of Work