The short answer: 12 hours.
I have heard about cats surviving up to 17 days without food or water. But that's supposed to be an accident or in a moment of tragedy. Such is the case when the owner has died or moved away assuming the cat was outside the house.
Cats should eat and drink every single day. I have heard of humans living and surviving being without food or drink for up to 13 days, that does not mean we do not need to eat and drink everyday.
Nobody deserves to starve, not even an animal.