When you first start the game, a local game account gets created. You can use this local account only on the device the game was downloaded to. It cannot be transferred to any other device and can quite easily be lost if you delete your local account or change it with another account.
You can save your game account by connecting it to Game Center. You are supposed to be logged in to Game Center with your AppleID by default:
- Go to "Settings" on your device;
- proceed to the "Game Center" tab and make sure Game Center is enabled (toggle on);
- continue with your Apple ID;
- go back to home screen and restart the Little Big Robots app;
- in the app, connect to Game Center via the in-game "⚙" menu (tap the "Connect" button).
That's it. Your progress is now secure.
The above will work only in case you don't already have another Little Big Robots account connected to your Game Center account. Otherwise, you’ll see a pop-up prompting you to choose between your old game account that is connected to Game Center, and your newly-created local account. If you choose the old one, you’ll lose access to the local account.
To save it, you should bind it to another Game Center account/AppleID.