The system only reads the RTC once at power up. From then on the time is kept via a free running counter. So it sounds like the RTC is working correctly, but not the counter.
The counter is usually clocked by a 50/60Hz signal from the power supply, so this may be issue. One suggestion is to move the clock source jumper, J300, to source the counter's clock from the system vertical sync pulse. This locally generated signal is divided down from one of the onboard oscillators, which have an accuracy of +/-20ppm at best. Therefore you may find the time drifts if the computer is running for any length of time. The frequency of the AC mains is extremely stable which is why it's ideal for such timing purposes.
Might fix the problem, though some Amigas won't boot without this timing signal being present. At least the A3000s don't, not sure about the A2000. Worth a look.
More detail on the A2000 jumpers
here.