I have developed an application that does require to do constant network activity. This Activity does the network connections thru an AsyncTask, sometime this work being do
Does your application have to be an activity? Can it utilize a background service?
http://developer.android.com/reference/android/app/Service.html#ServiceLifecycle
If you use a Service and make sure it stays active (by first starting it and simply not stopping it) the application wont be killed (unless it's extremely low on memory of course).
You should use a service instead of using an Activity to do work in the background.