I've been dabbling with Cait Sith's Astral Flow ability, Altana's Favor, and just wanted to share my discovery. It all started when I accidentally hit my Altana's Favor macro between Skirmish runs while trying to RR2 myself. It gave RR3 to my whole party. Well a few days later my friend informed me that he had not logged off or changed jobs, and that RR3 was still up. That was last Thursday (the 12th).
Well, last night I accidentally overwrote it with a fresh one, I guess he was closer than I thought he was. (I think he just wanted to be free to change jobs again!) That was about 2 hours before the 1 week mark.
So yeah. Altana's Favor RR3 lasts at least 1 week real time. My guess is it might last forever...