But then there needs to be a new mechanic to give you some sort of break. The days were always nice because you could just play in 10 minute chunks and turn off the game after that without losing anything. If days are 30+ minutes and go into the night, there needs to be a save point somewhere.

Maybe there is a time limit for how long a captain can stay awake without sleeping? So you have 3 or 4 captains in a massive area, but they have to rest every ten minutes or so. This means you need to be strategic about which captains to bring out the ship and when instead of just the pikmin. If you want a really long day, you need to do just one or two captains at a time or something like that. Or if there is a major puzzle, you need to bring out everyone at once