For the past 45 minutes, the notification of the most recent comment directed at me keep returning a few minutes after I've dismissed it by clicking on the inbox and viewed the comment.
It doesn't seem to be the case that the comment author has edited the comment so I need to be notified of the change. It has occurred so far with two different comments on different SE sites.
The problem seems to have gone away. I haven't gotten any duplicate notifications in at least a day.