Hi Trevor,
Let's take this one step at a time. You stated that the engine ran fine several times. That would mean that all the critical elements of operation were intact, fuel, compression and spark. Let's start with the carb. The carbs on these small engines are so simple that once the running positions are adjusted they rarely change, or clog up, so we can practically eliminate the carb. If it were a case of the engine running and getting hot then the problem could be vapor lock. When I first got my V-twin running it would start fine and run fine for about 2-3 minutes then the running would get erratic. By opening the fuel needle the engine would smooth out momentarily and then return to poor running. I have clear fuel lines on my engine and my friend noticed that as the engine was running the fuel was pulsating in the line. What was happening was the manifold and carb were getting hot and boiling the gas out of the carb. To remedy this I machined .03 from the ends of my manifold and made insulator spacers. This prevented the heat from creeping into the manifold and carb and boiling the fuel out. Just a thought.
The compression. You know how it felt when the engine was first put together and turned over. Does it still feel the same? If the valves were sealing well initially and the rings doing their job then those elements shouldn't have changed. It's possible that the valve clearance adjustment changed and if the clearance went away then a valve could hang open and lose compression. Easy check!
Cam timing. I don't know how the gears are affixed to the cams but if they are secure then you can rule out cam timing changing.
Take it a step at a time and rule out the obvious. These little engines can be frustrating to get running but you cleared that hurdle so it's probably just one element of the 3.
gbritnell