Battery backed RTC chips have coin cell battery backed SRAM also (such as CR2032, 36 cents here qty 1
http://www.dipmicro.com/store/index.php?act=viewProd&productCode=BAT-CR2032) that will run the RTC for 5 or 10 years.
Write a simple sketch that reads the time once a second, and stores that time to SRAM. Can even use the 1 HZ oscillator from the RTC to signal when to read the time.
The next second, read the time and store it again, and note if just 1 second had elapsed.
When you find a time that is more than 1 second different, send out a serial message, or display on a display, the time difference found - there's your power-off time counter.
Or, get a battery powered clock and a normally closed relay. When power is on, the relay is held in the open position, when power is lost the relay reverts to the normally closed position and the clock runs for as long as the battery holds out, or until power comes back. Don't know how you'd tell when more than 12 or 24 hours had gone by, guess that would depend on the clock used.
Hearing we might have a winter that makes up for last year's relative lack of snow.