Some players have told us that their devices have been taking longer to sign in to Game Center on all games (not just Alphabear), and that they are under the impression that it is an issue with iOS 9.
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 firstname.lastname@example.org if you're not 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.