Flashing Power LED - Not what you think...

My New Nintendo 2DS XL power LED flashes red as if the battery is about to run out, and shows the battery icon on the home screen with a single bar of power left.

The battery is not actually about to go flat though. Regardless of how much charge the battery has, the 2DS XL thinks it is about to go flat. I can play for hours with it flashing and it will be fine but I will have no idea when it might actually run out of battery, so realistically it can only be played while charging.

I can very temporarily fix the issue by letting the buttery run completely dry and then charge the battery. When I turn it on it will have a blue light and proper charge, but at some point goes back to flashing.

Would replacing the battery fix this, or is it more likely a connector or something else?