Is there something about the "new messages" indicator which causes people to fail to notice that they have new messages?
I think it goes to zero when you see the directory listing of the message, not the message itself. Then there may be a tendency to forget about the message if one doesn't read it right away.
I have six messages in my outbox. Two of them have been there since 2010. One more recent (but still a few months old) is to a MMember who still seems active.