Sure, you should have bugs documented somewhere but I'm not sure a bug that hasn't been fixed for x months needs to be there since it's a bug the team obviously decided not to care about.
I personally fixed bugs that have been opened for longer then that, so nope, they can get fixed. Plus, it prevents people from opening them again and again and again and again as they all notice the same thing.
I've fixed a couple Firefox bugs that were filed in Bugzilla 10-15 years ago. :)
At least one fix, however, upset some people who come to like the "incorrect" behavior over those 10-15 years. (In one case, I changed the filename of saved web pages from "index.html" to HTML <title> .html to match Chrome and IE behavior.)