The only correlation I could find was that the screen only goes off when my Ikea office chair is somehow involved.
So I suspected a loose contact somewhere. But no. No matter how much I wiggled the table/cables, everything was fine.
The problem was only there when I sat down or stood up, although the chair didn't even touch the table.
That was the moment I had my doubts. So I got another chair and tested it with it. No problem, screen stays on.
Took the Ikea "MARKUS" chair again, sat down - screen went off again.
HUH?! My chair has a feature that automatically turns screens on/off? I guess nice privacy feature?