OK, so the Hermit link is a little special. Each time, you get a request from the ema and you have to go track down the person who made the request and solve their problem before you can rank up the Link. Sometimes the Links take multiple days, but they usually just consist of talking to NPCs so you don't waste time by working on them, just do whatever step in the quest you're on before you do the S-Link/dungeon exploration for the day. Accepting the ema's request doesn't take up time either, the only thing that does use up your day is spending time with the fox AFTER you've fulfilled the request. The Hermit Link is one of the very few that you can do while it's raining, so I generally suggest saving turning in the emas until a rainy day when you aren't already going to the dungeon. Ranking up the Hermit Link is good, though, because the fox is who you buy SP restoration from, and it'll give you a discount as the rank of the link gets higher. The Hermit Personas are a little lackluster, but you can't have it all I guess.
