Hello,
This is an issue with the configuration of the monitoring system that you are using and not an email issue.
What software are you using for monitoring?
For systems monitoring I like to use
Spong. It's old, but I like it.
A newer alternative that many admins seem to like is
Nagios,
Can you configure the motoring so the checks need to fail x times over y minutes before generating an alert to your email and/or pager email addresses?
I've found that not alerting until 3 failed checks happen within 5 minutes works well for me.
Brief downtime due to network blips and other unexplained phenomenon will not cause you to be alerted.
-Raymond