Trouble with 99 Silverado 2500 6.0L cutting out while towing

I am having trouble with my 99 2500 Silverado 6.0L wanting to "Cut out" and sputter while towing, especially up hills when under a load. If you back out of the throttle if will not do it as bad but then of course you lose power and end up at 35-40 mph at the top of the hill. Has anybody else had any trouble like this where you can tell me what to look for. Thanks!

Have you checked your fuel filter?

No I haven't. I was thinking of that but thought that was probably to simple. I will check it out. Where is the fuel filter located at on this truck?

It's on the frame rail.If you do change it out make sure to put a rag underneath it so the gas doesn't eat the protective wax off the frame I used to pull the fuse to the pump and let the engine run until it died to relieve pressure on the line before I opened it up to remove the filter.