To state yet again: Exim has nothing to do with it. Once exim delivers the mail to the user, it never sees the email again. So the problem isn't exim.
Now let's try to get some common denominators since it's not happening to everyone.
If you're having the problem:
Which webmail client are you using?
Which POP Daemon/Imap Daemon are you using?
Which local email client are you using?
Is your local email client set to leave email on the server?
If so, for how long?
Jeff