Run some diesel kleen additive and then look at the Fuel filter housing. Also, consider installing a fuel lift pump/filter combo. We did this to our 2003 GMC. The factory pump is a little underpowered. If it is still misbehaving, probably the dreaded injector replacement.
See this thread:
Lift Pump ? - Page 3 - Chevy and GMC Duramax Diesel Forum
I can't recall the brand (not Airdog) that we went with , but it is a combo water separator/fuel filter type pump. Uses Caterpillar and Baldwin filters. Mounts on the frame rail right behind the cab.
UPDATE: Found the link to pump builder.
Duramax Fuel Filter Kit