I did some testing, and it looks like the only way to get a pet that old is by changing the system clock. For a pet to age that much while playing the game normally, you'd have to play it for over 100 years. To test this I adopted a new pet, stabled it, and changed the clock backwards by one day. When I launched the game again, my pet was 149,127 years old. My Palm didn't reset when I unstabled him, but he was VERY dead!

If you want to try to "save" your current pet, you might try setting your system clock forward until your pet's displayed age is more normal and see if you can unstable him. I must say, though, that Little Palm Pet is very sensitive to changing the clock, and there might not be anything you can do to save him.

If you want to just let that pet go and move on, select "Give Pet up for Adoption" from the pull down menu and start a new game with a new pet. You'll be taken to the adoption center and you can choose a new pet.