Hi

here is your problem.

The backup script you are using is not appending logs to the "2015-05-29-03:30:01.log" file placed in the same dir of your backups.
If you look closer you will see that file "2015-05-29-03:30:01.log" is empty.

Logwatch (the tool used to send you the daily mail with the logs) include that file in the section of the email, so thats why you are getting it empty.

Check out the .log file in the previous days backup directories, generated by the backup script shipped with iredmail 0.9.1 and you will see what you are missing.
I suppose you could add the logging function to the backup script you chose to use.

Could you please use the one in development version? It was fixed:
Https://bitbucket.org/zhb/iredmail/src

I think I have found the error

if [ X"${REMOVE_OLD_BACKUP}" == X'YES' -a -d ${REMOVED_BACKUP_DIR} ]; then
    echo -e "* Delete old backup: ${REMOVED_BACKUP_DIR}." >> ${LOGFILE}
    rm -rf ${REMOVED_BACKUP_DIR} >/dev/null 2>${LOGFILE}

    sql_log_msg="INSERT INTO log (event, loglevel, msg, admin, ip, timestamp) VALUES ('backup', 'info', 'Remove old backup: ${REMOVED_BACKUP_DIR}.', 'cron_backup_sql', '127.0.0.1', NOW());"
    ${CMD_MYSQL} -u"${MYSQL_USER}" -p"${MYSQL_PASSWD}" iredadmin -e "${sql_log_msg}"
fi

Above line:
rm -rf ${REMOVED_BACKUP_DIR} >/dev/null 2>${LOGFILE}
Should be changed to:
rm -rf ${REMOVED_BACKUP_DIR} >/dev/null 2>>${LOGFILE}

See attached patch file.