I use push notification (GCM) in my Android project.
According to GCM tutorial I implemented broadcast receiver and registered it in AndroidManifest.xml
According to Francesco Nerieri in this android-gcm thread:
So if you force stop the app, the intended behavior for ICS is for the app to not receive the message. In JB this means that GCM will also unregister the app, this is an unfortunate behavior and we are working to change this (the unregister part in JB).