Could be float in carburetor problems, blocked fuel filter, vacuum leak in fuel line, bad reed valve and leaking crankcase gaskets.
Of course, don't overlook possible plugs breaking down under load.
The carb floats will sometimes stick causing either too much gas or not enough, but either way, it will kill the engine.
Thumbs down, again? and yet the stupid ba***rd didn't give any ideas of his own as to the probable cause or solution. Yahoo should get rid of this damn feature.
Now,back to the problem. After reading again, if you're using a remote fuel tank, there might be an obstruction in the fuel line, or air leak, or the vent n the tank might be either closed or plugged.
This would explain the fact it runs for a while then quits when under load.
If it smokes a lot before stopping, then look for sticking float, if not, and it starts again after a short wait, then look for the fuel supply, and tank vent.
Some times the magneto will fail when hot, but his is rare and only gets worse, fast.