Your SMTP (mail) server is not allowing it to send the error notification e-mail.
Make sure that the administrators can receive the critical error notification e-mails.
Check SMTP mail server settings.
The 'unable to rely' is when an e-mail is sent from AMETHYST to the mailserver, but the mailserver is blocking it from being sent externally. Critical e-mails to internal e-mail addresses, might still be received. You will need to contact your mail service provider to correct this.
I must stress though: THE CRITICAL E-MAILS MUST GET THROUGH.
Please ensure that the critical e-mails is received as setup.