I made similiar experiences with a parallel EEPROM 28C16.

Every µC reacts crazy on lower voltage during power off or power on cycle.

So an expensive supervisor was a must on using parallel EEPROM or battery powered SRAM, RTC.

But I found a cheaper solution:

I use a serial EEPROM 24C16, since it was very unlikely, that a crazy µC can generate exact the right long serial writing sequence.

After this I detected no more any problems.
Furthermore it freed many ports for other usage.


So I would suggest to use a serial RTC.
E.g. the DS1994 looks very nice, since it contain already the battery and the crystal.



Peter