Jabber XMPP chat client for iOS with push notifications Chat Secure is working on iOS with Jabber but it doesn't stay active in the background (just for 10 minutes) so it is not really an alternative to the internal iMessage Chat.

Which app is able to save Jabber messages offline and send them as push notifications as soon as you are online again?

I use iOS 7 on an iPad Air
Beejive Pro with Push is the solution !