There are several islands in the game that are not closed upon completion of the main quest or when moving to the next map.

Balancer Island, Maze Island

These islands are the last in their storyline, there is no continuation yet, so the islands will remain open for now. You can temporarily use them as an additional source of resources. They do not affect the subsequent islands.
 
    

Mysterious Island

To close this map, players should find the mysterious egg, use it to improve the pyramid on home island and travel to Invention island. Make sure to finish all the side quests before you move to the next map!
 
 
Invention Island
 
This island closes after players travelled to Iron island at level 45.
 
 
Hippo Island, Raccoon Island, Ribbiting Island, Turtle Island
 
These islands are connected in one story line. In order to move from one island to another, you need to complete an additional task on home island - improve the flower bowl decoration. You can use the blueprints found on those islands in order to upgrade the bowl.