As soon as the engine quits pop the gas cap open and listen for a rush of air. The tank's vent could be blocked preventing gas to flow to the carbs.
If that fails check the J-Box. The procedure is outlined in the FAQs. They have the habit of developing cold solder joints. The links will take you to sights which show what to look for and how to fix them.
http://www.zggtr.org/index.php?topic=565.0