This problem can occur if signing in to Game Center or Google Play Games Service takes longer than expected. It should be fixed in version 01.10.00.
Please email firstname.lastname@example.org if you're still encountering this problem, because so far as we know it should be fixed for you.
At the time this article was written, version 01.10.00 wasn't yet available. Please see if this helps as a workaround to the problem:
1. Open your Settings app and sign out of Game Center.
2. Launch Alphabear and dismiss all screens prompting you to sign in to Game Center until you reach the Event Select screen.
3. Click the Game Center button on the Event Select screen to sign in to Game Center.
Please try that.
Please email email@example.com if you're able to get around the problem. It would be great if you can include a link to this page so we know which troubleshooting steps you've already tried.