I'm sorry that Cheeze It decided not to come back. I hope you and Cinnimon get along very well.
You should not stable your pet unless you plan to be away from the game for awhile. The purpose of stabling your pet is described in the game's instructions:
If you have to go on vacation, or will not be able to care for you pet for a while, you can STABLE him (in the PREFERENCES menu). The pet will continue to age, but will be cared for.
I never stabled most of my pets, and they do just fine overnight. If you don't have time to really play with your pet, just a quick check on him for feeding and cleanup should be enough. A little combing will give you extra "brownie points" too.
