I opened the door using the ball on the first button, stepped on the 2nd button a few times, then rolled the ball away, got my companion to stand on the first button, rolled the ball to the 2nd button, at this point the door was still open. Then I pushed my companion off the button and the door closed and didn't open again when the button was pressed. All of this happened without exiting the room, then I exited and returned and it was still stuck, then I took the screenshot only after I exited and returned a couple of times.