As mentioned in this forum a few times, the Downtown is well known for having a weak charging system. The regulator-rectifier is especially problematic as it can't seem to handle the power requirements of the scooter and is located above the exhaust pipe so it overheats easily. I have replaced the regulator twice and stator once during my 300i's lifetime.
In the Downtown 350i Kymco has noticed this issue affecting 300i models and replaced the faulty design with a different regulator. One thing to mention is that it looks much more robust with a bigger aluminium heatsink and thicker wiring. It has been relocated to the left side of the bike above the airbox to allow better airflow and cooling. This adds to the LED front indicators and LED brake light and a 55W headlight (35W+35W on the 300i) which helps further reduce current draw.