Hi Belinda

There is the ability to send an email to a specified role that an attempt has been made on a quiz.

The permission to allow is emailnotifysubmission. The email can contain a number of fields and content of the message can be changed by modifying the message using the language modification.

A link to the attempt number can be included in the email so this can be reviewed by the email recipient but there is no facility to restrict this to being sent only if the quiz is failed in all attempts.

See http://docs.moodle.org/19/en/Quiz_submission_email_notification for more details

regards

Craig