When you say "starts right up, runs fine" that's when you turn the key on, not just hook it up and it does shut down with the key, right? I'm wondering, just how good is a Hayg pump. Is there a possibility that you have water in the gas? Send me you bad one so I can test it, if you want, I won't damage it with out getting back to you for permission and I'll send it back if you want. Do you have the equipment to test for resistance, volts, amps, etc.
The way these pumps work is they move the gas past the armature, the bearings and the brushes, I suggest mounting it vertically so if you DO have water in your fuel, it can drain back out if it's in the pump when you shut down and if there is a strong possibility that you have debris in the tank, maybe a filter ahead of the pump, I prefer and have my filter after the pump in case the pump adds debris to the fuel. As for Rocmoc's suggestions, do check for voltage when off and that the ground wire has a good connection to ground, I doubt that a low voltage would be there via damaged wire, the pump needs too much power for leakage current to damage it.
I lean toward contaminated fuel or jump pumps, but just sitting for a week shouldn't kill even a poorly built pump, and these don't look like junk. How much alcohol is in your fuel? What do the sales people say?
Kinarfi