The first place you should start when diagnosing exim errors, is
to look in the log files. The first log is /var/log/exim_mainlog, which
will include information about mail that is accepted, rejected,
relayed, etc … The next log is /var/log/exim_rejectlog, which stores
information on messages that were rejected. The last is
/var/log/exim_paniclog, which is where exim logs to if something
drastic happens and exim either cannot start, or has to shut down
unexpectedly.



If you have looked at the logs, and are still unsure of what the issue
is, you can run a test delivery. If you wish to test where the failing
is in a piece of mail/delivery sent from the IP of 1.2.3.4, you can run
the following command:



exim -bh 1.2.3.4



This will run a fake delivery in debug mode, showing you all the rules
that a message would pass through, and what the status of those tests
are.