According to the User manual for your camera : the date and time may be returned to the default settings if the camera is left without the battery for a long time.
This seems to indicate that there is another battery (usually user inaccessible) which is used to maintain certain settings, predominately the Date and Time.
How long is a long time? It should certainly be longer than the recharge time of the main battery.
I agree with you the settings backup battery has failed.
Here is a link which shows the teardown of a WG3. At 16 seconds into the video I believe that you can see what I think is a button battery on the mainboard, (directly above the red end of the screwdriver handle). If it is a standard button type battery, these are usually not rechargeable but have a long life, especially if their function is usually performed by the main battery. They only have a very low discharge current when the main battery is removed. In some older PC's the CMOS battery was of the same type and usually lasted 6-8 years before replacement was necessary. Mind you it is a lot easier to replace them than to replace the one in the camera by the look of it
Planned obsolescence - perhaps?