Sounds like the dreaded pinched vent line. It's a common occurrance and easily repaired. Next time the machine dies (and you can do this while rolling if you're careful) unscrew the gas cap. If it fires right up the vent line is the culprit. You'll have to pull the seat and lift the tank, just a bit, and look for the black hose under the right side of the tank along the frame spine. It tends to get pinched between the tank and the tank mount fittings. Seems many dealers cause the pinch while assembling out of the crate. It will run (as you've seen) for a few minutes, so as far as the shop is concerned, it's good to go. And if they don't give you a full tank to start with, you don't find out about it until later. Only when the vacuum from the clogged vent becomes strong enough to stop the flow will everything stop. It happens faster with a full tank since there's less air to compensate. Many of us have pinched the hose after a simple lifting of the tank for almost anything.
And if you're absolutely sure it's not pinched, but the symptoms point to the vent, check for a clogged one-way-vent valve. Follow the vent line down until you come to a black plastic filter looking device. It's a one-way-vent. Some guys hate to think the factory would put anything on a bike that's worthless, so there's an argument that you really need this piece, I needed it to see how far I could throw it... got about 25 yards (it's pretty light plastic).
