With the problem you describe, the first thing I would be checking is fuel flow to the carb. Your problem could be caused by a couple of different things, bad fuel filter, bad fuel pump, bad fuel cap, partially plugged fuel line, etc. If you have a fuel filter that is clear, quickly check to see if you have fuel in the filter when the engine starts to die. If the vent on the fuel cap is partially plugged, you can try quickly opening the cap once it starts to die and see if it will continue to run. If you have a vacuum fuel pump, the pulse line could have a crack which opens when the line gets warm. You could also have a vapor locking situation, but that would be very rare. This type of problem will drive a service tech to pull their hair out, as it is an intermittent problem, which may not show you while he is trying to replicate the problem and he has to figure out how to show it without charging you hours of labor without a solution. It will help us and the service techs if you can narrow down the problem by trying a few simple checks first. You may get lucky and find it quickly or drive yourself crazy during testing. Good luck and let us know if you can narrow the problem down.