Should you choose to fight, you've got 300 minutes to run into them again, or they'll have fully recovered. If you encounter them again and fight them, the counter is reset and you have another 300 minutes to find them again. If you bypass them, the timer keeps counting without being reset. You can keep track of idols you've encountered in the 勧誘リスト (the blue button on the left, when you get into the event's welcome screen) - remaining HP and time to recover are listed there.
Manage your stamina and pick your fights, too. If you're getting low on stamina, and you're sitting on a full meter, it may be best to fight the first idol you run into then rest. Your ATK will refill while you do. Conversely, if you've just blown all your meter, you can take that opportunity to rest up and recover ATK and stamina.
Got it, thanks. Now I know where to look... It's kind of a pain banking on running into Ryo. She's tough to find.
EDIT: Cleared her out, but not before I finished the area, leaving myself running 6 stamina a pop to try and find her again.
Also, anyone know how to clear that other Iori event? Not the one where you join the group, but the other one where you seem to have to post things. I can't read kanji, so I don't really know what I'm supposed to be doing, but I hit all three buttons and made all three posts (and I know I did because I was hit with the one-hour timer between them) and I haven't been granted any of those things, especially not the Iori. It's been about a week and none of it has shown up in either gift list.
