It would be possible to use EEPROM to keep track of progress through the program. I don't see that the RTC solves anything really - you would still need to know when the program started in order to figure out where you were up to from the current time. If you need to have a persistent store to record when the sequence was supposed to start/end (and then have some way to program and display that) then you might just as well have the sketch store the time remaining when it was told to start and then count down as time elapsed. Given the low timing resolution needed it would only need to count down the number of hours remaining, so I don't see EEPROM life being an issue.