I think your best and probably only realistic option is Dynon support, since the backup battery is fully integrated and controlled by the display. Either there is some unusual parasitic drain, or the system is erroneously detecting a low battery voltage.
My Skyview can sit for weeks without being charged, and even occasional power up via the backup battery, and this has never resulted in a warning message for a low battery.
Good luck, hopefully it is still under warranty and please let us know the outcome!