Apple’s new iOS 5 includes a feature that allows text messages to be delivered directly to iOS devices, bypassing your carrier’s cellular network completely. It’s nice, insofar as it includes delivery confirmation messages. So, iPhones know when a message is being sent to another iPhone, and automatically uses this new service called iMessage.
The downside is that if you connect automatically to a wi-fi network that has blocked ports, you’ll find that iMessage text messages aren’t delivered. They often just pause midway through sending.
Also, you may find that other push notifications for other apps (like Facebook, Calendar, etc.) don’t get pushed to iPhones.
Not to worry, it’s an easy fix (so long as your network administrator is amenable to fully supporting iOS features like this!).
iMessage and push notifications works over the APNS (Apple Push Notification Service) channel. That is TCP Port 5223 outbound to 126.96.36.199/8 (Apple). Your admin will know what to do with this information!