On June 19, Twitter has said it will be disabling “streaming services,” which is how third-party apps like Tweetbot and Twitterrific can stream the timeline and send push notifications. The replacement, the Account Activity API is not available to third-party developers:
The new Account Activity API is currently in beta testing, but third-party developers have not been given access and time is running out.
With access we might be able to implement some push notifications, but they would be limited at the standard level to 35 Twitter accounts – our products must deliver notifications to hundreds of thousands of customers. No pricing has been given for Enterprise level service with unlimited accounts – we have no idea if this will be an affordable option for us and our users.