How about the float in the carburator. maybe the float is sticking and the motor shuts off after the carb. runs dry. ( maybe a minute or two ) Try and tapping the carb lightly with a small hammer. the vibration may lossen the valve from the ceat in the carb there by letting the float droping and allowing more fuel into the carb. Qustion ?? will it keep running after it is started for the second time ???