[RayChez1]

It sounds to me like a plugged up fuel filter. There should be a filter probably close to the fuel tank. Follow the fuel line back from the engine to the tank and I am sure you will find it.
I had a simular problem on a 1988 Ford F-250 truck and I didn't even know that such a filter existed. It was mounted on the frame to the truck close to the fuel tank.
I hear a lot of people talk about vapor lock, but I don't believe there is such a thing. The problem is usually something else, like a bad fuel pump, plugged fuel filters. I would say also fuel injectors, but usually when they start to go bad the engine will miss, like if you were to disconnect a spark plug wire. But you mention that the engine stops, so it leads me to believe that it is your fuel filter. The filter on my 1988 truck was all medal and about three inches in diameter. You should be able to find one probably at WalMart.