Thanks Dave, but my Windows 10 is running fine reliably and without any other (noticeable) problems.
I have found simple way to get the effect. I now have DXView pinned to the Task Bar. Click on it to open it. it can be seen in Task Manager as an App. When it's opened fully, close it from the Task Bar by clicking on the X in the corner of the popup.
It the moves from the Apps in Task Manager to Background Processes.
Like I said, the work round is not to close DXView from the task bar. Simple.