Remove the fuel bowl housing from the gas tank and make sure the inlet to the bowl housing is not full of crud. They take in gas from the bottom of the tank. Flush out the tank good when you have the bowl housing out.
When the inlet to the housing is plugged the engine will run a minute then stop. After a few minutes the gas from the tank will slowly push gas out of the bowl to the carburetor and the engine will run untill the carburetor goes dry because of resticted flow from the tank.
Hope this is the cause of the engine dying.