2000 Chevy Impala turning off?

If it were a blown fuse, then it wouldn't turn on at all.

Sounds as if you have a short in your wiring that's allowing the control circuit to finds its own ground. However, I can't be too sure with out checking your system.

The body control modules on these cars are notorious for causing weird issues. And the only way to be sure is to get my hands on it and test each circuit.

Sorry, but electrical issues are sometimes very hard to track down, especially explain. If you're handy with a multi meter, then you can probe your circuits. If not, you'll have to take it into a shop.