[kodfodrasz]

* I guess You can create a background worker handling persistence, which runs until completion even if the UI has been closed. (I have not used UWP yet)

* IMHO save/don't save dialogs are an usability antipattern.

* Tray icons are also something of a remedy of the past. They are now replaced by background operations and live tiles. I can see why those can be problems, I can imagine the usecases you would solve using those tools, but the new app model is build around a slightly different workflow.

But if you do not like the way to solve it as it is intended in the new app model, the solution is: report it/upvote it. If you tell your problems here, then some members of HN community will know it and understand it, but it is unlikely that it will be acted upon by Microsoft. For that you need to have your voice heard on their forums. (eg. feedback app, uservoice...)