Ahhhhhhhhhhhh, they stay on for about 30 seconds.

They also revive when you:

• Open a door
• Turn the key to any position other than full off
• Turn on parking/headlights
• Open the trunk

I get the idea from your post that you expect the displays to go out right away - I've never timed it but I THINK the timeout is about 30 seconds. If they NEVER go out, I would think most likely that you have a bad door or liftgate/trunk switch.