We are using Ignite and I didn't change the logic anywhere until I started trying to resolve the problem.
What you are describing sounds like the way I believed it should work, but it doesn't seem to do that for us. I set up a separate alert to email me directly when servers go offline, and I have messages in both "Alert Message on Success" and "Alert Message on Failure". I receive the email when it goes offline but I never receive the email when it comes back online.
Thank you for describing how yours is working and letting me know we have a problem instead of just a wrong assumption on how it SHOULD work. I'm going to create a support ticket to have it resolved.