Check Settings -> Display -> Screensavers: I can set a screensaver there in case of “Playing”, “Not playing” and “Off”.
You can also set the time for the screensaver to start. I am not sure if this is identical in the SBT as I am using a Pi with Squeezelite and JiveLite GUI.
Does it disconnect, when the display shuts down? In that case you might want to try to extend the time for that.
I think this is in Settings -> General -> Automatic Screenlock
Maybe you misunderstood.
I’m talking about two different things.
The first is about the SBT that goes into the status “paused” after an album or song or playlist comes to it ends. In this status the album picture remain on the SBT where you would expect the SBT to go back to “idle”. In my case show the time.
This issue was not present when using Roon from my HTPC. Nor with LMS.
I have check the screensaver options on SBT also.
If I’m the only one with Roon on a Qnap with a SBT attach, we may wait until someone else can confirm the same behavior.
The other issue is related to iPad.
Where my request is if there is a way avoid the iPad to disconnect from the server. I get a message connection lost, and it take some time to reconnect.
The same issue was present with iPeng and LMS on my HTPC.
Or is there a way to speed up the reconnection time between the Roon server and the iPad Roon app ?
Are you talking about the iPad settings ?
I just tried it on my Squeezelite.
When I set the ScreenSaver for “Not Playing” to “Current track” the screen will remain on the last played track. When I set it to “Analog Watch”, it will display the watch after the playback has finished.
(I am not sure if the wording for the englisch menu entries are 100% correct, as I have my menu in german and was too lazy to switch it to englisch)
If you mean something different, I might indeed have misunderstood you here… 
Can you explain your issue with the iPad more precisely? I tried it on my iPad and it stays connected as long as the display and the app is active. If you switch the app or turn off the screen it will loose the connection and needs to reconnect. I think the iOS has to be accounted for that and background apps can’t keep the connection alive (somebody can correct me here, if I am wrong)
So, yes: In my second point I was talking about the iPad settings…
Did some more factory reset as well as reinstalling SBT with EDO, and reboot the Qnap as well.
SBT now behaves as I expect it to do.
Previous error message on SBT that could not connect to my NAS also disappeared.
Now I will not touch anything more 
Thanks anyway for your assistance.
With iPad I will if needed get back to you later if needed. But I’m sure there is some sort of timer hidden somewhere like it is with every application that is restarted on an iPad.
Not sure if a user can adjust the “keep alive” setting.
Also now the connection time to the Roon app seems very fast. After killing the app, and restart it again, very fast.
No more saying connection lost, trying to reconnect (so far).