Hmm, K-Star has touched on the initial tests and if you are not mechanically inclined then perhaps it is time to take it to a scooter (and more particularly) a Vmoto specialist. You could try ringing the Vmoto headquarters in Perth and getting a mechanic from them. Avoid the mechanic who quoted you $1100 over the phone. Has has not even seen the scoot and is quoting you that much without even having the foggiest idea about what the problem is...
Because it runs for a while, I doubt it is a fuel delivery problem related. I would have figured that if fuel-related, then it would not start at all or be very "spluttery". So perhaps onto heat-related problems. Not quite sure on the design of the carb (about the one thing I haven't pulled apart yet), but perhaps when it heats up, settings are changing, choke is turning off and mixture is leaning out and scooter dies then..
Have you tried pulling the spark plug and holding it near (near, NOT touching) the frame while cranking the engine?? You should get a nice big fat spark leaping from the plug to the frame. If not, you have some ignition problems and could possibly be a duff CDI module (gubbin what does the sparking)
My advice: take it to a scooter mechanic and get it looked at.
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