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Thanks for the feedback.
Generally, Outlook client uses Autodiscover record to connect to Exchange Online, so I suggest you check if the Autodiscover CNAME record exists in the domain and if it works correctly. Please refer to the method 2 in http://support.microsoft.com/kb/2404385.
If you haven’t added the Autodiscover CNAME record, please add it to the domain and then check if the issue persists. Please refer to http://help.outlook.com/en-au/140/cc950655.aspx.