Push seems to works differently for different IM apps.
Beejive IM - the app runs in background for it to receive push messages.
Trillian IM - same , the suspend feature does not work for me , does it work for anyone ?
IM+ - this one works , has an option to keep connected even when you exit the app. Push messages come in even when the app is not running.
I am almost tempted to switch back to my iPhone 3GS, beejive worked great on it.
running Samsung Galaxy s II , android 2.3 . with all the battery issues.