Sounds like vapor lock, which is caused by the fuel getting hot and turning from liquid to vapor. It's far more common in summer, but winter fuel vaporizes more easily than summer blends. When the fuel cools back to liquid, the bike starts again.
Since the fuel pump and filter are in the tank, the likely place for the vapor bubble to form is in the fuel line external to the tank. This would be the fuel line from the tank, the fuel injection portion, and the return line to the tank. When these cool down, all's good.
I would consider replacing the fuel filter (it's inside the tank), and while you're in there, check all the tubing for the fuel pump system. Some bikes have had problems with the tubing developing holes, and the symptoms can mimic (and might be) typical vapor lock. Check the pump to make sure it's at full strength.
Last item: What you described is
classic vapor lock, and is
nothing like a bad starter clutch. If the stealership guy was working from the same symptoms...I wouldn't trust him in the future.
