Diagnosis
The thermostat is not receiving sufficient power from the C (Common) wire connection. The backup batteries are draining to run the display and Wi-Fi.
How to Fix It
Verify the C wire connection at both the thermostat and the furnace control board. At the thermostat base, remove the display and confirm a wire is connected to the C terminal. At the furnace, open the panel and trace that same wire to the control board's C/COM terminal. Ensure the connection is secure at both ends.
If That Didn't Work
The connected system transformer may be undersized or faulty, failing to provide the necessary ~24VAC. Use a multimeter to check for ~24VAC between the R and C terminals at the thermostat base with the display removed.
Heads Up
If your original thermostat didn't use a C wire, the wire may be tucked in the wall. You must connect it at both ends for a permanent fix; relying on batteries will cause recurring disconnections.