Missing alarm notification in Notification Center on Mac mini

The other day I had set an alarm to go off. It went off but the notification banner disappeared and was no longer visible to stop the alarm sound. When I moved the mouse to the upper right to activate the Notification Center the banner was not there. The only way to shut it off was to go to the Activity Monitor and kill the Notification Center. What went wrong? Is there some sort of setting on the Clock app where it will show alarms going off that you can turn off? Is there some sort of setting I am missing?

[Re-Titled by Moderator]

Original Title: Alarm notification disappeared.