Hello,
I had IOS 5 installed on my iPhone 4 and no notifications from Twitter. Everytime I go in the app, the notifications are disabled!
I updated the iPhone to IOS 6.0.1 (10A523), restore the backup and no twitter notifications! I deleted the app, clean cookies and reboot the device, still no notifications. This is very anoying!
I am going to restore it as a new iPhone! Save my sms and pictures, contacts are in gmail.
Cheers,