My bet, is that it's the afm. This is just a guess but I had a very similar problem. There is a strip of metal that when contact is made or broken I can't remeber which, that fuel is cut. Its called the "angel" switch, its there so that in the case of an accident the fuel pump will shut off and not flood the crash site with gas.
Here is what I think you should try.
1st. Check and double check your AFM connections for frayed wires or shorts.
2nd. If that checks out, then run a hot wire from your fuel pump to your battery so it cannot shut off. This IS NOT SAFE! I only want you to do this to see if it is a fuel pump power related problem.
3rd. If 2nd is ture that pop off your afm cover and bend back the tab of metal just a bit, so that it breaks contact as soon as the afm flap is moved.
Give those a shot and get back to me.