The reason why e-mails are not going out from your LMS domain for live class invitations, course and test enrollments, forgotten password requests, and other places is due to an incorrect custom SMTP mail server settings.
To troubleshoot, go to "Account & Settings --> Mail Relay" and set "Yes" to use BrainCert mail server and try sending the email hook again.
Select 'No' to use your own mail server and use the correct mail server credentials to setup your outgoing email delivery. Click "Send Test Mail" button and confirm you have received the test mail before saving the settings. Contact your e-mail hosting company to get the SMTP server hostname/IP address, Port number, and connection details (SSL/TLS).