I play around a bit more (no pun intended lol) and I think I came to a reason why it's doing it. What sess said, it something to do with the drive "mounting".
If playing a game that require constant streaming video/audio/loading (ie. Mario Kart Wii, Super Smash Bros. Brawl), it will unmount the drive ~1 minute into the game.
If playing a game that doesn't require constant streaming and only loads data when it needs to (ie. moving to "another level" and/or entering/leaving an area), it won't unmount itself unless you keep doing something that makes it loads data constantly (ie. entering/leaving a house in Animal Crossing). Though I find this strange because I played ACCF for an hour with no problem before. @_@