When migrating to Exchange 2013 from Exchange 2010 the Archive Manager ESM account fails to login to any Exchange 2013 mailboxes but it can still login to the Exchange 2010 mailboxes fine.
In the ESM logs you may see error 600 along with 'Invalid Request'.
You may also see the error: "Autodiscover Discover returns null" or "Error processing mailbox. System.Exception: Unable to determine Exchange connection settings"
When an Autodiscover request is performed the request undergoes what Microsoft calls Mailbox Anchoring, the credentials of the requester are used to determine the CAS server that should service the request.
If the ESM account has a mailbox in 2010 the request is forwarded to a 2010 server which cannot correctly service the request.
If the account running the Archive Manager Exchange Store Manager (ESM) service [typically this is ArchiveMgr_ESM] has a mailbox then that mailbox needs to be moved to Exchange 2013.