It sounds like something is not right on the server. Look at the STProxy SystemOut.log and I am sure you will see exceptions, probably SSL related. Can you verify you have done the following?
- Created a database for STProxy.
- Created the tables in http://www-01.ibm.com/support/docview.wss?uid=swg21663020
- Opened gateway.push.apple.com, port 2195
- Opened feedback.push.apple.com, port 2196
- Applied updated APNs SSL certificate http://www-01.ibm.com/support/docview.wss?uid=swg21641787
"It seems to be more a client problem on the IOS Device in point of view because the link to the server is working. As long as the device is not in standby you get all informations about new messages." This is how it is designed to work.
Read my blog, it describes how it works. The crux is that if an IM is sent to a user that is on iOS and the app is paused the IM is saved to the database. The STProxy server sends a message to the APNs. The APNs has a note of the devices "number" and the APNs then sends a message to the device in the form of a notification on it's screen. The user clicks on the push notification on the device, this wakes up the application brining it to the foreground. The app then connects to the STProxy server and it then retrieves the IM from the database. Once the IM is sent to the device it is removed from the database.
Either your device is blocking notifications for the app or you haven't configured something correctly on the server.