I've just tried Hexen in Vavoom 1.32. I got the Emerald Key. I opened the door, retreated from the swarm of ettins. The door closed. Now I can't open it again !
I get no message about missing key, and it seems present when I press TAB (map screen), but otherwise the door doesn't function. By the way, the door closes so fast that even on Squire (lowest difficulty) it bounces off Ettins' heads. It starts closing immediately after opening.