Is the fuel getting very hot in the fuel line? That usually happens when a fuel line is near exhaust or some other extremely hot place. If so it can vaporize and cause vapor lock. Odds are there is water in the gas, or the gas is bad, or the carb is bad. Another thing to check is if the gas cap is blocked up and not allowing air into the tank. Those gas caps can go bad too.
Possible fixes: Get fresh gas, check the gas cap, clean the carburator, make sure the float is not sticking.