Stumbles on hot start

It was my father's truck and it was only driven a couple times a month for short times. Truck runs great. I have one problem that I cannot figure out. When it is cold, truck starts and runs great. After you drive for a while and shut it off, then the problem happens. If you get back in to start within a few minutes, it starts fine. If you let it sit for fifteen to thirty minutes, it starts, but stumbles and most of the time shutdown. It is as if it is starving for gas. When you turn the key again, truck starts and runs fine.

I have checked timing, water temperature, vacuum leaks, fuel pressure and all seem to be normal. It has a new EGR, idle air control and new O2 sensor. Those I have replaced in the first few months I had the truck from check engine lights at various times. I have had the fuel system cleaned, both intake and injection system.

I am lost. Any ideas?