We operate a 2002 Chev Express G1500. We had dealer replace fuel pump in 2008 to address a similar problem. During 2009 problem reappeared and was very annoying as our unit is a delivery vehicle with many stops and starts. My brother and I had a very reputable independent mechanic go over the engine and check the specs on the fuel system. Turns out that the intake manifold was leaking, a bit, but enough to release gasoline onto the engine. we had the manifold re-gasketed. Then they tested the fuel system. The newly replaced pump was not producing sufficient startup pressure..60psi (must have 64psi according to Chev/GM 2007 service bulletin specifically onthis issue). Problem was when the vehicle was cold it started ok. Once shut down any re-start did not receive sufficient pressure to serve the engine demand.
We replaced the newly replaced pump in late summer 2009. Aftermarket, high quality pump spec'd out to meet the Chev service bulletin.
Van now starts and runs like new...six months later.
Our biggest issue: the dealer would not acknowledge they installed a deficient pump, did not know about service bulletin and messed up the intake filter on the "in-tank" pump when they installed the unit in 2008.
Hope this might help and save you big bucks. Pumps and installation are not cheap.