If the indoor screen of your WS5029 is suddenly 'chewing' (rapidly discharging) batteries* it's most likely to be because of an issue with the outdoor sensor (hygro-thermo sensor under the louvered housing).
When there's an issue with the outdoor sensor, the screen tries to maintain connection to the failing outdoor part and consumes lots of power in the attempt to seek out/maintain connection.
In these cases replacing the sensor is the solution, once the new sensor is installed the system returns to normal battery use.
*These weather stations need a quality alkaline battery for function, please do not use 'cheap' or rechargeable batteries. These (cheap/rechargeable) batteries can be used rapidly.
In the case of a rechargeable battery, overtime, as the battery doesn't charge as well they cannot offer the required voltage for your weather stations function.