Once Stitcher is paused and in the background, none of the app's processes are running, therefore the app does not use up battery. If you are concerned with having the app still being visible while not using it you can swipe away the notification and/or clear Stitcher from the "Recent Apps" list.
Adding a 'quit' button is unfortunately not an option. We've been working very closely with the Google design team throughout this process and they explicitly said not to add a quit function as they are trying to get apps to utilize the Android OS's natural handling of apps in the background. By using the device back button to exit the app or by clearing Stitcher from the "Recent Apps" list you can more definitively close the app.
Android apps like Stitcher enter a 'sleep' state when in the background. So in our case, if you pause whatever show you're listening to and put Stitcher in the background we shut down almost completely and wait to be resumed. We don't adversely affect memory or battery consumption while in this state.
We apologize for any trouble and please note that our Android developers are discussing a workaround feature that might better satisfy both our listeners' desire to Exit the app and to comply with Google's standards.