Persona 3 has taught me a lot about High School in Japan. I never knew that the entire day's education consisted of either answering one question or taking a nap on your desk to stay in good dungeon crawling condition.
I've made it to floor 4 of the dungeon. It's seriously intimidating, that place, especially since I don't know shit about Persona fusion right now. The dungeon is actually what the school transforms into during the hidden hour (Dark Hour).
If you explore a dungeon for too long, your party members get tired and you should leave. If you keep pushing it, they can get "Sick" status, which is what happened to one of my party members, even though I thought I got out quickly. I don't know how many days I need to avoid the dungeon for in order for him to recover.

