ASKER
Exchange is the server side of a collaborative application product that is part of the Microsoft Server infrastructure. Exchange's major features include email, calendaring, contacts and tasks, support for mobile and web-based access to information, and support for data storage.
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This issue might be occurring as you database or mailboxes are having issue.
Is you exchange is updated with latest Service Pack and Roll-ups? If not, Please update it first and keep behavior under observation.
else
You can create new database and move mailboxes from effected database to new database.
Please refer below article to better understand Exchange Mailbox quarantine:
http://thoughtsofanidlemind.com/2014/01/27/mailbox-quarantining-in-exchange-2010-and-exchange-2013/