If you have 25 devices/apps or more with granted permission to interact with twitter, once you go to add a new interaction notifications will not be allowed.

See here https://support.twitter.com/groups/55-troubleshooting/topics/234-mobile-apps/articles/20169333-managing-push-notifications-on-twitter-for-android

At the moment I cannot activate push notifications on twitter for android on my Note 3.

I just wonder if this is a method whereby twitter charge dependant on needs. Or maybe they will allow free up to a certain amount of connections?