It sounds more like a slow drain on the battery, which can come from a few unexpected sources. Disconnect the ground side of the battery, with the key off, and hook up a VOM set on the 20 VDC scale. If it draws ANY current, then you have a problem. Here are the places to start looking for a solution.
1. Ignition switch has a dirty starter contact: even at a stop, it will drain about half an amp until the battery dies. Replace the switch, but not the lock.
2. Dirty battery cradle. If it is full of grease, or has any hint of contact from the positive post to ground, it can slowly drain the battery. Pull the dying battery, put it on a slow trickle charge, and scour the battery case with baking soda solution. Paint with insulating paint and return your battery.
3. Frayed battery cable. An intermittent short from the positive lead can make your battery beg for mercy and possibly send your scooter into the scorch mode.
4. Cold climate. If your battery gets too cold too much, it can sulfate itself to death. Heated garage makes sense as a place to store your scooter.
5. A "hot" lead where it should be cold. Miswiring can fry a scooter. Your dealership may have a trained HD electrician. This is a job for a pro, not a bro.
