My 2007 TBA kept dying and acting like it was running out of gas, same as yours , open the gas cap and start right back up. Turned out to be the tip over valve. A small cylendrical check valve that mounts inline in your gas tank vent tube . It is located right behind your carburetors. The valve gets stuck and the gas tank wont vent. Dealer took mine off blew some air through it and freed it up and reinstalled it. No problems since. I posted a thread in this forum about this and got a lot of response from people saying they had the same problem. Good Luck.
