No, it is not the battery (should really be more correctly called the cell).
A defective battery, meaning of defective construction, is unheard of. A
flat battery is unlikely. The batteries (or cells) used on motherboards are
of the rechargeable variety. The discharge characteristic of these
rechargeables is that they operate almost at full strength till the last
moment, then the voltage drops off *abruptly* to near zero, unlike the
traditional torchlight batteries (zinc alkaline; for that matter, the car
battery, i.e. lead acid, too) which drop away more slowly; the light dims
and gradually goes out. Have you not noticed your mobile phone, which is on
rechargeable batteries, can just shut down on you unannounced; one second
you are yakking away and another second the phone is dead as a dodo?
The slowing down (or speeding up) of the clock time (the 'real time clock'),
which misleadingly gives the appearance of the *gradual* dying of the
battery, is the result of the *cumulation* of errors in the 'heart beat'
(the in-built timing oscillation) of the real time clock on the motherboard.
This oscillation 'beats' at a rate which depends on taking regular samples
at fixed set intervals from the computer main oscillation (the 'system
clock', i.e. the CPU's 'heart beat'), so mirroring the system clock but at a
much slower rate. The interval between the sampling has, for some reason,
been knocked off its correct value. Once this error is eliminated, i.e. the
'intercept interval' is reset back to its correct value, the clock should
run without the error in the 'heart beat' and so should run correctly.
The rechargeable cell on the motherboard lasts for years, probably outliving
the usable life of the computer. I wonder how many people have actually
changed a dead cell on the motherboard!