Does it cut off after the engine has been run and then shut off for a while? Is the engine still running after driving and cuts off only when shifting into reverse?
If it cuts off going into reverse after sitting, you may be experiencing vapor lock. It should also cut off going into drive if it's vapor lock. Engine temps will rise considerably when shut off after it has been driven for a while. This is called heat soak. The hot engine has no coolant circulating through it and there is no air flow through the radiator or engine compartment during this period. This can cause the fuel in the lines to vaporize. You will have enough fuel in the carb to start the engine, but once that fuel has been used up, the engine will cut off. There will be no liquid fuel in the fuel lines, only a vapor. The fuel pump will eventually pick up liquid fuel and refill the carb. The engine will once again run.
Check to see if the fuel line is making contact with any hot engine parts. Especially between the fuel pump and the carb. Check to see if the fuel line is close to any exhaust components. If there is a clamp to hold the line that is also attached to the engine, insulate the line with a split piece of rubber hose at the clamp. You do not want any metal to metal contact with the hot engine. If the line is close to an exhaust component, move it or place a section of insulative sleeve around the fuel line. This insulation can be found at speed shops or through Summit or Jegs in various sizes and lengths.
You don't want to rule out vacuum leaks either, but a vacuum leak would exist at any time that the engine is running. The vapor lock issue should appear in either forward or reverse after a hot engine shut down. | 
