Symantec Messaging Gateway (SMG) might not be able to communicate with Microsoft Office 365 cloud service (e.g. *.outlook.com mail servers) when SSL/TLS encryption is enabled.
It has been observed issues might be caused by use of potentially insecure or expired certificates. Please also see:
Please make sure certificates used for SSL/TLS communication including CA certificates, are valid and meet current security standards.
Please note: if issues cannot be resolved by replacing certificates, following workaround can be implemented:
Please uncheck Offer TLS client certificate in SMG advanced SMTP options section: Configuraton -> Hosts -> SMTP -> Advanced Settings
In addition SSLv3 option might need to be enabled if you are on 10.6.0-3 or 10.6.0-5 build, please see following article for further details:
When SSLv3 option is disabled, Symantec Messaging Gateway (SMG) fails to negotiate cipher suites with MTAs that support SSLv3 cipher suites only
Please contact Symantec support if further assistance is needed.