When your app goes to the background Android has the option of keeping it around or closing it completely at any time. Often when a separate app is brought to the foreground that is resource intensive, Android will start killing off other apps that are in the background and not actively doing anything.
Really the only way to stop Android from potentially killing of your app is to have a Service running in your app that requests to be in the foreground. Of course, by doing so your app will be required to display an icon in the status bar.
The takeaway: Your best bet is to store a key representing your currentUser in a Preference or datastore rather than depend on a global variable being held on your Application object.