I have had that happen -- quits then cures itself. Maybe a stuck float the vibrated loose? Vapor lock in the gas line? -- did you pull the line off at the carb to see if gas flowed out there? Was the spark plug wet with gas or dry? If dry, next time try pouring a little gas in the spark plug hole and see if it starts -- if it does it is a lack of fuel problem.
The spark on a TW is very weak looking. I guess it gets stronger at higher RPM -- but at idle it is barely visible.
When you figure it out lets us all know. I never did figure mine out but it hasn't given me one iota of a problem in a long long time so I don't think about it.