You need to store a Thread object as member of some other object with lifetime longer than Activity.
Two ideas for you:
a) It could be a member of Application (http://developer.android.com/reference/android/app/Application.html)
You may have problems with this, if you don't have a Service running. There is no guarantee that your application won't be killed (as example if any system dialog will pop up on top of your activities)
b) It could be a member of Service (http://developer.android.com/reference/android/app/Service.html)