eMails failing to send

When we send schedules out to our team, on occasion the system fails to successfully send the email (could be for a load of reasons). Currently this failure is shown in the 'System Events' window, however this window is also populated with loads of other notifications, most of which are not really system failures. When Care-For-IT has a genuine system failure, can we have an email sent to selected email address(es) to notify of the system failure please?