Help ????

 

I will guess the dieing is a vent problem. If the cap isn't venting the gas can't flow. If the gas isn't flowing the carb is empty. An easy way to test this is, right after it dies open the gas cap, quickly. If you hear a hissing or sucking sound, there is a vacuum in the tank.

 

My guess would also be a lack of fuel flow into the carb bowl. Could be float and valve stuck, clogged screen inside tank... or lack of vent as already mentioned.

What happens when you open the drain on the carb? If this is on the right track, then I would expect good flow of gas until the bowl empties, then it would slow to a drip or trickle that doesn't flow enough gas to keep up with what the engine uses...