It will lose its face-downness when it gets exiled:
400.7. An object that moves from one zone to another becomes a new object with no memory of, or relation to, its previous existence. This rule has the following exceptions.
so it's an instant again. That means it will stay exiled:
400.4a If an instant or sorcery card would enter the battlefield, it remains in its previous zone.
304.4. Instants can’t enter the battlefield. If an instant would enter the battlefield, it remains in its previous zone instead.