Another reason why it dies is it might be flooding out ..
This can be caused by a float level that is too high. If you havent dropped the motor , removed and cleaned and adjusted the carb, it would be a good idea to do so.
Also check your air filter. The bike won't run right unless all parts are there and everything is clean and tight. There are no shortcuts, but once you get things right it will run great just about forever.
BTW, the "petcock" in the on/off valve thing on the fuel tank. If fuel flows into the carb, the petcock is not the problem.
(To check for fuel flow all the way to the float bowl, remove the right side cover and theres a little hole to stick a screwdriver through the chain sprocket and through the swingarm .. Unscrew (one or two turns) the drain screw down on the carburetor's float bowl. Gas should come out of the rubber drain tube onto the floor)