Minimum voltage to avoid EEPROM corruption for ATMega328P
As an addition to the accepted answer:

Regardless of the causes for EEPROM corruption, you always face the potential problem that you are not able to complete writing a sequence of bytes.
Consider a 4-Byte integer value. The BOD will only "guarantee" that single byte corruption won't happen, however it won't prevent the controller from shutting down before the whole 4-byte value has been written, effectively corrupting your data.

To be on the safe side you have to implement some kind of "commit" mechanism. This would involve a checksum to verify that you data is valid and a mirror copy of the data, to make sure that one dataset is always valid. If the checksum fails on startup, you can fall back to the backup. The "valid and active" dataset can be "marked" with a single byte.