I just had a similar situation with random dying and starting. Mine always pointed to the fuel pump. To make a long story short, my problem was a bad ground at the fuel pump connector. Checking for power at the inertia switch lit a test light and showed 12 volts, but the pump would not run. Putting a load at the inertia switch ( a 12 volt motor I had laying around) was how I finally found the problem. Before you replace an expensive pump (as I did), you might want to check for a bad ground.