When you bind your Service to Activity with BIND_AUTO_CREATE your service is being killed just after your Activity is Destroyed and unbound. It does not depend on how you've implemented your Services unBind method it will be still killed.
The other way is to start your Service with startService method from your Activity. This way even if your Activity is destroyed your service won't be destroyed or even paused but you have to pause/destroy it by yourself with stopSelf/stopService when appropriate.