Have you tried squeezing the fuel bulb after it quits to verify its not the fuel pump or otherwise starving for fuel? Make sure fuel is getting to the carb. You can remove the line at the fuel pump that goes to the carb and squeeze the bulb watching for fuel.
Also, check for spark after it quits. You could have a coil thats bad, sometimes they fail when hot. Even though it has two coils, one dead one can make starting a twin near impossible.
If fuel is getting to the carb, and its got spark, but still wont run, you have to start digging deeper. Run a compression test. Sometimes they can leak between cylinders when hot. You may have to remove the carb and see if the fuel is physically getting into the bowl. I dont know how that could be intermittent, but you just have to test everything.