PC Mainboard - CMOS Bios Battery Circuit
The battery backup circuit is the battery OR'd with a feed from the 5V standby line via 2 diodes (usually regulated down to 3V), 

So that while there is power from the power supply (plugged into the wall and switched on at the back) it does not consume any of the battery capacity, 

It is only when the wall power is gone that it begins consuming capacity from the watch battery, this is why they tend to last longer in computers that are regularly used, as its essentially only self discharge (the shelf life) that determines when it will run flat

As to why your battery voltage is falling so quickly, its possible that something is partially shorting out the battery and discharging it (it could be flux residue or some dust buildup on the PCB across the contacts) in all other use cases it should take atleast a month to bring the voltage near 3V, (not much capacity in that top 0.3V)