So is it a site issue? I'm inclined to think that this isn't on the site since I've experienced more than shoddy connections with my DSi and yet never seen a glitch like this before....
The thing is, I've never encountered a thing like this before. That's what's off-putting about it.
Just out of curiousity, what device are you running on? If it's a rather laggy device, then it's possible that the request to delete the notification doesn't go through before you reload the page.
I'm not sure why that's the case, but I'd prefer comment notifications be manually deleted (the way they are), because sometimes another comment(s) come in after your comment reply.