Thongs to look for. The CMOS cell is not needed when the computer has power.
That means that if the clock is gaining or losing time while the power is on, it can not be the fault of a dead battery. The clock works without the battery.
So, that would lead to one of these conclusions:
1. The clock crystal somehow got way off frequency. Quartz crustal oscillators have accrual or better that 100 parts per million. So, it would lose maybe 7 seconds in about 24 hours. Maybe. How much time does it lose?
2. There is some kind of software that is getting into the clock registers. Now that would be near impossible for an 'accident'. Do you have a prankster in the house?
3. There is a small creature, maybe a mouse or insect, that l;icks the pads of the clock chip and make it reset the time.
4.You are losing ;your mind.
Oh, there is another one. If the machine been dropped it may have fractured the quartz crystal. When that happens, the circuit may go into a 'parasitic' mode where the clock is much faster than normal. That is so rare nobody will believe you.
If you have a freq meter, check and see of the crystal is running at 32,768 Hertz.
https://en.wikipedia.org/wiki/Real-time_clockthe oscillator's frequency is 32.768 kHz.[7] This is the same frequency used in quartz clocks and watches, and for the same reasons, namely that the frequency is exactly 215 cycles per second, is a convenient rate to use with simple binary counter circuits.