Since I encountered this exception now at 2 customer installations, I have decided to say some things about it here: I don't know why - but in both cases MS CRM Exchange Router stopped working after 2 weeks (this is no joke). Of cource users were complaining that emails didn't show up in CRM anymore. When I checked the event log, I found many error messages of the same type. They were all some kind of
Microsoft.Crm.Tools.ExchangeConnectorService.ExchangeSinkServiceException because of unauthorized access (401). After some google and NG search I tried several workarounds like changing the service credentials, checking security groups (PrivUserGroup), giving mailbox rights, or playing around with delegation. But the only effect was that I got another ExchangeSinkServiceException. This exception stated that the email message that should be attached to CRM could not be checked.
The next thing I did was to find out how Exchange Router and CRM process emails. It turned out the router calls a webservice on CRM server (CheckIncoming ) with the Message ID. Since the second exception was some kind of server error (500) I figured out that CRM could have problems connecting to Exchange Router email box. So I decided to run the Exchange Router Service with the credentials of the user who owns the MS CRM Exchange Router mail box (because this user should not have any problems connecting to his own mail box). I don't know if this is correct, but CRM seems to connect back to Exchange and does some checking involving the CRM tracking token (or something completely different ;-). In addition I added the user to the PrivUserGroup so that the user account has sufficient privileges to create emails in CRM. Doing that the first webservice call did work correctly. Using a second webservice (DeliverIncoming) Exchange Router then created the email in CRM.
So if you encounter this exception and don't find a solution, try the following:

1. Add the user account owning the CRM Exchange Router mail box to PrivUserGroup.
2. Change the credentials of CRM Exchange Email Router Service to this user account.

Hf ;-)

P.S. I really don't know if the above explanation has something to do with reality. Probably it is complete nonsense. :-)