How can I get the car to stay on

Obviously you have a fuel supply problem. Check the metal fuel line for signs of rust or leakage, and check the rubber hoses for dry-rotting and leaks. If there's any leaks, the fuel pump will draw in air instead of fuel from the tank.

If no leaks are found, remove the inlet hose, install a fitting, then see if it pulls any vacuum when cranking the engine. If it does not, suspect the pump, or the push rod that runs the lever on it if your engine uses that.

If there is vacuum at the inlet you can try connecting a piece of fuel hose to it and placing the other end in a can of gas to see if it will draw fuel. If it does, check the pickup sock in the tank to see if it is plugged or collapsed.