Auto theft function malfunction?

I have a 2004 chevrolet colorado that refuses to start intermittently. I don’t see any flashing lights, but when it does this, won’t start, if I wait 10 minutes after the initial crank, it starts right up. My mechanic thought it was the auto theft function, but it starting happening again after he fixed it 6 months ago. So now he wants to replace the starter $220, or spend $200 for a program that will allow him to “disconnect” this feature… It’s a pain. If you are running late to somewhere, and it won’t start, you end up being 10 minutes late. But after 10 minutes… it will start right up.

What exactly happens when it fails to start?