This issue occurs when you provide a mail-enabled user with a delegate or service account in a Microsoft Exchange Web Service (EWS)-based application in an Exchange Server 2013 environment. This issue will not occur when you use EWS-based application impersonation.
This issue occurs because, when Exchange Server 2013 processes a FindItem request, Exchange Server 2013 tries to log the request. That causes an attempt to look up mailbox attributes. However, a mail-enabled user does not have the mailbox attributes. Therefore, Exchange Server 2013 throws an "ErrorNonExistentMailbox" error.