1992 Mazda 626 won't stay running

First if you have old gas in the tank you need to purge it. extreemly low octane gas will cause a lot of problems. Second Is this a carbed engine or Fuel injected? if carbed( it would seem if pumping the gas keeps it running) pumping a fuel injected engine would do nothing because it only opens a butterfly valve and pumps nothing. Bad gas will gum up yur carb fast. Either way, Make sure the fuel pump functioning at the correct pressure. A week fuel pump will also atribute to this problem. So... Start with new fuel and check the fuel pump volume.