If I were to guess, I'd side with Drew: the gas tank is "oil-canning." The tank can't vent, and it starts holding a vacuum that fights against the fuel pump. Since the pump is only pushing 2psi, it doesn't take a lot of counter-pressure to overcome it. The longer it runs, the greater the vacuum, the less gas gets through, the leaner the mixture is, and the worse it runs as the plugs foul. Eventually, the vacuum counters the pump entirely, and the engine starves out.