I've never opened the dashboard of a civic so I can't really give you car specific advice, but... I've got a '01 prelude, and the double din mounting unit actualy unscrews and then screws back in. At the moment, mine is unscrewed because I havn't finished everything back there yet, so whenever I pull the empeg out it does what you describe.

Apperently there is something you can do with a strap and the back of the docking bay to secure it, but havn't done any of that because I've got both DINs filled so there isn't my room for stuff to slide around.

Matthew