When a Silverlight plug-in is displayed in full-screen mode, keyboard events are prevented from being passed to keyboard event handlers in the application. The only valid keyboard input that is acted upon is the set of keystrokes that return the Silverlight plug-in to embedded mode. This limitation of keyboard input during full-screen mode is a security feature, and is intended to minimize the possibility of unintended information being entered by a user.

Source: MSDN: Silverlight Full-Screen Support