I have had this problem. When it quits, unhook the fuel line - none will come out. These tanks are very hard to clean and keep clean. Sediment floats around and settles plugging the line after a period of running. I fixed mine by putting a stand pipe in the settling bowl so that it would draw gas from 1/2" off the bottom.
I've heard that the condenser in the mag would cause the same problem. I have never seen this. Almost everything on running is fuel related from my experience.