RE: [exim] Exim not delivering email to mailbox

>Is this a problem with Exim or Courier-IMAP?

Impossible to tell, since it is not possible to know whats wrong until you
have shown us the exim logs of the transaction.

But I would _guess_ that Exim is delivering the mail to a plain mail-spool
file on your system, which most likely is not what you want.