Android 4.4 has a bug:
Swiping an app away from the "recent apps" list kills the app's process and all background work that the app is doing.
If the app had a notification icon, it will stay stuck in the status bar, giving the appearance that the app is still running ("adding insult to injury").
This is a change in 4.4, and I believe it's a bug (as opposed to an unexpected, but intentional change) because the status bar icon stays there.
So, if you use push mail, do not ("I repeat, do not") swipe AquaMail away from the recent tasks list.
Please refer to this discussion for further info:
https://groups.google.com/d/msg/android-developers/H-DSQ4-tiac/EOVBgM7R3lMJBeing an Android bug, it has to be fixed by Google.