[Exim] Some incoming port 25 connections not processed

By looking at system logs (perro/tcp.log and daemon.log) I can tell
that there have been two computers connecting to my computer on the
SMTP port, every 16 min or half an hour, round the clock, for the last
several days. No mail appears to be processed; nothing appears in the
exim logs, even with log_level=6. Other mail is delivered normally,
even other messages from the same computers, and logged as I would
expect.

I'm stumped trying to find it out why no messages get through, How can
I tell _exactly_ what is going on when the remote hosts open port 25?

I am using Exim 2.05 in Debian 2.1.

Thank you for any clues you can supply.

Liam Healy