Thought I'd post this as I'm now having the same problem with my scooter after putting on a performance exhaust that I was having prior and had just never quite solved.
Issue was that when I rode for more than about 15 minutes when the weather was hot the scooter would just die on me sometimes when I stopped at a light or even die sometimes when I cut throttle to go around a corner in an intersection. Then it won't start until the scooter cools off. Manually choking the scooter by covering the snorkel doesn't help in this situation.
I figured it was running lean and getting too hot and just thought I'd tackle the issue after I installed a performance pipe and rejetted. So I've done that. Rejetted and also put a new auto enricher on it. It starts okay when cold. Starts easily when warm but still will die sometimes idling at an intersection and then won't start again until it cools off.
Today I had started it up after it had sat for an hour and then drove it about 3 blocks. Weather was about 75 degrees. Sitting at a very long light, probably idled for about 2 minutes, it died. Would not start at all. Waited 5 minutes. No start. Waited 5 more. Still nothing. Waited about 15 more minutes and it started after maybe 20 or so revolutions of the starter.
I'm pretty frustrated. I used a propane torch the other day to see if their was a vacuum leak, but wasn't sure where all to place it. I might take a spark plug wrench with me to see if I have spark. Maybe something in the cdi fails intermittently when it's hot.
You all have any ideas? My wife has had it with me calling her and saying I may need a ride home. I got her a Honda Metropolitan and that thing is so dependable.
Thinking of taking it too a shop, but wondering what they might do that I haven't done and worried how much they will charge to chase an intermittent problem.