Wow, just shutting off sounds more like an ignition problem. Maybe the igniter? Since it only happen initial after cold start and now it's getting worse with time, you could try heating the igniter with a hair drying (not too hot) and/or cooling with a can of circuit cooler to see if you can cause a failure. Also, what is the voltage at the battery while the bike is idling?
I never thought of the igniter. Thanks. Where is it located? The battery is always connected to a tender, but I'll check the voltage while idling tonight. Thx again!