When you log out basically what happens is that the server will destroy your session in the server memory/session state etc. If there is a new request from the same client the server will read the session id cookie and try to match it with one of the existing sessions. If this session will not be found then we will get the exception you are facing.
Having a SilverLight application this is basically a client application which will not send any request to the server until it really requires is ( Service call). I think you should send a log out message to all of your application instances to log out the user also on the client side everywhere else.
Maybe this links will help you
Can silverlight detect or communicate across browser instances?