No your not missing something. The game last as long as you want it to or until you delete & start a new one. But as you still need 1 butterfly hang in there, it will show up. There likes & dislikes are just that, there is no whale meat etc in the game. It just gives them their own characteristics. You can open another game if you go on main screen & choose another player & go about that game different than the way you played your 1st one. But keep checking in on your 1st villagers as the butterfly shows when you least expect it to, it did with me as mine was last collectable to find also. Good luck!!!
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My granddaughters are one of the precious things in my life & the other are my grandsons.