Is there a cron job running that might be sending notifications?
less /var/log/cron
(I see _daily_ log entries similar to yours in /var/log/qmail/current on my system which appear to be generated by "logwatch")
Do these files have any more information?
/var/log/qpsmtpd/current
/var/log/sqpsmtpd/current
Is there anything in /var/log/messages at the same time(s) as the qmail log entries?
Is there anything interesting in the Maildir for admin?
cd /home/e-smith/Maildir
find .
Can you find the emails using something like this?
find / -ctime -1 -type f -name "*$(config get SystemName)*"
If all else fails, does some process log errors if you stop the qmail service for 10 - 15 minutes?