Small Engine Troubleshooting Problems? Ask a Mechanic Now.
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Can you tell me if the carburetor has a fuel shut off solenoid on the bottom of it? If so this is most likely your problem, if you aren't getting a constant voltage to it when the engine starts then it will shut the fuel off going through the carburetor and the engine will not continue to run.
The solenoid itself is about an 1 1/2" in length and will have a wire going to the bottom of it.
I would start by making certain that you are getting voltage to that solenoid all of the time when the key is turned on or the engine is running. If you are not then that will be your problem.
If you will unplug the wire going to the solenoid you will then be able to test for voltage at the wire when the key is turned on. You will need a voltmeter to do the test or check.
Be certain that you set the meter to read DC volts and you should have around 12 volts on that wire with the key turned on.