While you are limited in time to complete a certain archipelago, you will have a chance to re-visit it later.
If you are not satisfied with the results you had on some archipelago that is already over, you can restart it with some gems. In order to do so you need to open the archipelago map by clicking on the map icon in the bottom-left corner of the screen:
Then you need to select an archipelago which you want to restart and press a restart button:
Please note: the rewards for completing a certain amount of islands is only claimable once. You will be able to earn the rewards you did not receive during your previous visit to archipelago yet you will not get extra rewards.