I had a problem with a notification that just wouldn't die, until I figured out what I needed to do to get rid of it. I created a ticket on one character, got the notification on another, which makes sense being account wide, so you'd think closing it on that second character would work as well. But it kept showing up again until I went back to the character I submitted it with and then when I closed it, it stayed closed.

I don't think it's ideal we should have to do that- if the reply is account-wide, then closing it would intuitively be as well. But if you have multiple characters perhaps that's why yours won't go away so it's worth a shot.