I'm with DanDaMan that a poorly vented gas cap could easily be causing this problem. And it's something that a mechanic might actually NOT think of exploring. The symptoms that you describe fit the situation well. If there a strong vacuum inside the tank because the cap is not venting, eventually flow of fuel to the carburetor will stop. It happens on lots of bikes. Mechanics can waste hours looking for some mechanical/electrical cause, and not make this simple check. I would not assume that this has occurred to your crack team.

Dan's right: What a shame it would be if everything else is working fine, and it's something as simple as this!

Good luck!