This is something we see primarily VSTS On-Premises. So far, it's always been because the customer's SMTP server is not responding to us to indicate that the mail was sent within our timeout period. When this happens, we treat it as a timeout error. But, sometimes the message actually does get sent. Since we have no way of knowing this, we will retry sending the e-mail later. There is a VSTS registry key that the customer can set to extend this timeout.
To extend the timeout to 60 seconds, run this command in the configuration DB:
exec prc_SetRegistryValue 1, '#\Service\Integration\Settings\SendTimeout\', 60000
To revert back to the default timeout value:
exec prc_SetRegistryValue 1, '#\Service\Integration\Settings\SendTimeout\', null