I have the exact same problem like this guy posted:
I am running Exim 4.69 with DirectAdmin
I installed it through pkg_add from this link: http://files.directadmin.com/service...xim-4.69-2.tgz
My server's OS is: FreeBSD 7.1-PRERELEASE
Everytime I have to change the ownership of /var/log/exim/ to 'mail', and its always back to 'root' after a day or some hours.