ATmega's EEPROM has a lifetime of 100k write/erase cycles. The program stores current time every 10 minutes, giving it ~2 years of lifetime. It looks like the clock will die long before you.
A colleague once told me about a bug in it's audi where it would write the current volume of the radio to an EEPROM after every volume change. So, after a few years, the car stopped remembering the last volume setting when turning the radio off and on, because the EEPROM died.
Just kidding...