If it's cutting out like that I would say either an air leak or somehow the fuel isn't getting to your motor.

An air leak is most likely the seals in your carb. I've never had the problem so I can't tell you how to find or fix it. If you search the forum for T15 air leak you should find it. A member called 46u has sealed a few motors that had the problem. you might want to PM him.

As for the motor not getting fuel. It could be your tank too. After it stalls. Is it easy to start back up?