I think you need to map out what is happening and then see if an issue is highlighted.
I think you are saying this :
Scenario A. App started, press Home Key, press Multitask Manager, re-enter App and it is still at the point that it was at.
Scenario B. App started, press Home Key, select App from icon, re-enter App but it starts all over again..
You will need to ensure that you have logged the Exit and Entry points for both scenarios and see if there is a difference. Just put some logging in place
to see what is going on - and of course be connected to the App itself. Are you seeing different messages in Logging when the App starts and stops for instance? Put logging in Activity Create, Activity Pause and Activity Restart, one of those will be the culprit and after a bit of investigation you usually see or realise why the App is acting as it is.
Are you able to trace through these two scenarios? Using the debugger? That might help. Maybe for some reason it isn't using the Activity Pause or Activity Restart Subs as you expect it to.. It's probably somewhere in one of those two that it's going differently.. You'll need to step through the code and/or put some breakpoints in place, but remember that for Activity Pause (I think) you won't be able to step through the code.
As mentioned by Erel I use Statemanager for my code, but this is mostly for when people use the Back Button as opposed to the Home Button as they work differently of course.