Help with Game Center login.

I have an issue with Game Center login that I can't find an answer to. I have the Game Center authentication script in my main camera on the Menu scene. The problem is that when I open up the app on my iPhone connected to WiFi, the banner indicating that Game Center has logged in doesn't show up, meaning that it's not authenticating, thus I can not access to the leaderboards UI.

BUT when I turn the WiFi off and relaunch the app, the banner pops up and I can access the leaderboards UI (without the leaderboards showing because no internet is available).

So why is this happening? I have another project that uses the exact same script and it works perfect, so I'm guessing that the problem isn't script-related.

Here is said script:

 import UnityEngine.SocialPlatforms;
 
 function Start () {
     Social.localUser.Authenticate (ProcessAuthentication);
 }
 
 function ProcessAuthentication (success: boolean) {
     if (success) {
         Debug.Log ("Authenticated");
     }
     else
         Debug.Log ("Failed to authenticate");
 }

I'm running both projects on an iPhone 4 running iOS 6 and an iPod Touch 4 also on iOS 6, both with the same result.

Can somebody help me? Thanks!