I would like to share my experience about using Paho Android service 1.0.2.
Neither my Android app nor Paho Android sample can reconnect to MQTT broker after closing the main activity. It means the app never receives the push notification after closing the main activity. It's something really confused behavior. The official site states "The Paho Android Service is an interface to the Paho Java MQTT client library that provides a long running service for handling sending and receiving messages on behalf of Android client applications when the applications main Activity may not be running."
Looks like the Paho android service just is a library in Android, it can not remember the broker information and reconnect to the broker after the service is restarted by Android OS(Android OS might kill the service then relaunch it later for releasing resource). I have to implement myself android service which consumes Paho Android service to reconnect to the broker then subscribe the topics if necessary.
Paho Android service only can reconnect to the broker without cleaning session and the network becomes available from unavailable state. But it can not reconnect to broker if something wrong(such as server side error response) happens causing the connect lost. Anyway I can monitor the MQTT connection lost event in my Android service, and reconnect to the broker.