logger_myslow.log is rotated by /etc/logrotate.d/zimbra entry. I don't recall if this is in the 3.1.x releases, if it isn't you can append this to zimbra logrotate.d file.
Code:
/opt/zimbra/log/logger_myslow.log {
daily
missingok
notifempty
create 0660 zimbra zimbra
compress
size 5000k
rotate 3
}