Like has been suggested, verify that you actually have fuel being pumped to the IP.
I had the exact same symptoms on my 6.5L several years ago; I nearly pulled my hair out trying to figure it out. In my case, I was able to determine it was running out of fuel - I still had the factory fuel filter, and I could remove the top of the filter, and see the filter housing was empty. I was able to run the lift pump manually, but no fuel would come from the tank. Give it a few minutes, and it would eventually pump fuel again, but only for a short while. Everything had been replaced - fuel lines, filters, lift pump, fuel pickup. Turns out it was the aftermarket pick up sending unit assembly I had replaced a few months prior. It used an inferior "sock" (screen on the end of the pick up tube) that would slowly collapse shut after pumping fuel and then block the pick up tube, preventing any fuel from getting pumped from the tank to the IP. Let it sit for a little while, and the sock would relax, allowing fuel to start flowing and then the process would start all over again.
I ended up have to scrounge up an OEM "sock" and putting on the end of the pick up tube. Never had a problem since.
Casey
1995 K1500 Tahoe 2 door, 6.5LTD, 4L80E, NP241, 3.42's, 285/75R16 BFG K02's; 1997 506 block; Kennedy OPS harness, gauges, Quick Heat plugs, and TD-Max chip; Dtech FSD on FSD Cooler; vacuum pump deleted, HX35 turbo, Turbo Master, 3.5" Kennedy exhaust, F code intake; dual t/stats, HO water pump, Champion radiator; Racor fuel filter