Hi Bo,
the PCF8523 has a battery backup input VBAT pin. I see you are using a supercapacitor as a backup supply. The battery switch-over circuit monitors the main power supply and switches automatically to the
backup battery when a power failure condition is detected. Accurate timekeeping is maintained even when the main power supply is interrupted.

The reset shouldn't happened if the switch over circuit and backup system works correctly.

If the reset is asserted, then yes, the CAP_SEL bit in Control_1 is set to its default value 7pF.

Is it possible for you to check the CAP_SEL bit value in the Control_1 register? Or is not possible because of non functional I2C communication?
Before you test the RTC have you enabled the battery switch over function in the PM[2:0] bits? Could you measure voltage on the VBAT pin during your test?
If the reset had been asserted and the CAP_SET bit in Control_1 register is set to 7pF instead of required 12.5pF there should be a change in oscillator frequency. Could you connect a pull-up resistor and to the CLKOUT pin and measure the oscillator frequency. For the 7pF the frequency should be higher, than the 32.768kHz, because it takes shorter time to charge and discharge the 7pF capacitor, than the 12.5pF capacitor.

With Best Regards,
Jozef