This quote is from the news post.
"How do you 'lose' without the 30-day time limit of the first?"
The same way you lose in every other game without a time limit. You die at the hands of the enemies or in this case you can also lose all your Pikmin. In most games you can't lose you can only stop playing when you get bored or when you feel the game is too hard for you to continue. It's the same here. You lose when you quit playing.