2wd 6L. 1500HD

It sounds like a problem with the fuel pump for your 2003 Chevrolet Silverado, the check valve or a crack in the flex line in side the tank from the fuel pump to the outlet pipe. Replacing the fuel pump module should correct this problem. You should try and confirm the problem in inside the fuel tank by connecting a pressure gauge directly to the fuel line from the tank. Key on, pressure should build and hold after the key is turned off.