I have completed a pair of projects which have RTC requirements, and can tell you from hard earned experience that power interruptions happen.
The don't have to be blackouts... a thunderstorm going thru your area may have substation lightning hits which interrupt the power briefly, but enough to reset the micro.
Dedicated RTC circuits will continue running happily from its own battery or supercapacitor.
I can vouch for the DS1307...Low cost, very simple to use, I2C communication, and since it already provides the seconds, minutes, hours, date, day, month and year with leap year correction, it greatly simplifies your firmware requirements. In a SMT package with a 32Khz SMT crystal, its footprint is even smaller than the backup battery.
You also get for free 56 bytes of battery-backed RAM, which you can use at your leisure for any variables you don't want to loose. I use them for running time registers. Since a running time register is constantly being updated, you would put large stress on an EEPROM used for that purpose.