Were you under load each time? If the fuel pump is failing the first place it shows up is normally when the engine is under load, demanding more fuel, and the pump can't keep up. Another similar instance is when the engine is hot and the pump can't pump enough to make up for hot fuel vaporizing which results in what is often called "vapor lock". The fix in both cases is the same. Rebuilding/replacing the fuel pump. If this doesn't match your situation it could be debris in the float bowl. To check that, remove the cover and look. If you have debris, clean it out and put a fuel filter ahead of the carburetor to catch the debris before it gets to the carburetor.

It did happen under a load.  Does the glass bowl on the fuel pump have a filter inside?  If it does where can I get a replacement?

@buckaroo01 

Hi John

If you have the original style pump with the glass bowl on top, there should be a brass screen right up top once you remove the glass.

Unless it's damaged, you should be able to just remove it and blow it clean.

If you DO need a replacement, they show up on Ebay.

Hi John

See my post under 41 fuel pump. Your intermittent fuel problem may be dirt or debris in the fuel system causing fuel passages in the carb to plug up or the same thing going through the fuel pump check valves causing them not to completely seal which will cause insufficient fuel volume getting to the carb. Worn or dirty check valves in the fuel pump can do the same thing. Same thing if the inlet of the fuel pump can't pull enough fuel because of a restriction in the line between the fuel tank and fuel pump. This inlet restriction usually shows up as an old rubber fuel line that has deteriorated over time and is collapsing or can be debris floating around in set the fuel tank.

All fuel pumps can be checked with a fuel pump/vacuum test gauge preferably off the engine. Both fuel lines need to be removed from the fuel pump to do this test and all fuel out of the pump. The inlet will pull vacuum and the outlet will make pressure. The max reading you get should hold steady or very slowly decrease. If the vacuum or pressure drops back right away, then the check valves are not completely sealing because of wear or debris on the check valves. A freshly rebuilt fuel pump after I get done rebuilding one will usually hold up to 12+ inches of vacuum on the inlet and 2-3 pounds of pressure on the outlet when operated it by hand. 

This can show up in your situation where the fuel pump volume is not enough under load to keep up with the carburetor. Once the engine dies and you restart the engine, the fuel pump volume is more than enough to fill the carb and idle the engine until you get to the point down the road that you basically run out of fuel in the carburetor. I saw this a lot in my early days as a master heavy truck technician as medium duty gas powered trucks are usually always under full load and the problem was either an inlet fuel restriction, a small hole in inlet fuel line sucking air or a worn out fuel pump.   

@robert-marx "If the vacuum or pressure drops back right away, then the check valves are completely sealing. " Bob is this what you wanted to post or should it  be "not completely sealing"?

Steve, I believe that's a typo and should be "aren't" instead of "are". That's how I read it anyway.

Thank you, Steve and Tiny, for pointing this error out. I have fixed it. If you see something else that you think is wrong, just let me know.