Why would a 1999 Suburban start then shut right after a few rainy days?

Your security system is malfunctioning and putting your Suburban in a temporary lock down. It is shutting down your engine right after start each time. In a few hours it will reset and allow you to start your Suburban again. Needs a new distributor cap. May be a loose fuel pump electrical connection. Located on top of the fuel tank. Requires dropping the tank to access and inspect.