There's a distinction between the Activity state and application state.
The Instance state is associated with the Activity, and can be used to store information temporarily to re-populate an Activity during a single lifetime of the application. I.e., it's useful when your Activity is being destroyed by the OS. But when your application is killed (like you're doing from the task manager), the instance state is wiped.
If you want to store information persistently across multiple lifetimes of the application, you should use the SharedPreferences framework.
See here for more information: http://eigo.co.uk/labs/managing-state-in-an-android-activity/#How-to-Store-State-Information