Is this a freeBSD box? (Just curious since the FreeBSD port builds exim to usually run using user "mailnull" and group "mail")
Take a good look at your exim logs and see who is sending..
/var/log/exim_mainlog
/var/log/maillog
Also the message that you posted really doesn't mean much, since it depends on how much resources you have to begin with and what you set it to alert you. Make sense?
And I would also recommend taking a good look at your domlogs /etc/httpd/domlogs for the periods where you are getting these resource limit emails. You can search them using grep.
If you think there is something strange going on, and don't know what to do, think about hirign someone who can help you out. There are plenty of people around here offering such services.
