At some points your question is not clear.
What I want to do is persist this array, but only for this screen,
then user exists that particular screen data will be forgotten.
By this line it seems you only persists the data only when the activiy is running ( in foreground or background). So in that case there is no need to store the data elsewhere rather than the class variables. So if this is what you want then may be you are calling the asynctask in onResume. SO in that case call the asynctask in onCreate.
But if you want to persists the data even after the application is closed then you can use SharedPreferences to store the array.
It will be more easier to know your problem if you can post your codes.