With the current release no log rotate occurs. When the free disk space is less than the 90% of the partition capacity the logmanager stops to work and the logs are no longer stored. In the future, log rotate will take place in the same condition (90% of the capacity) instead of stopping the logmanager process.
At the moment, Zeroshell can receive and store syslog messages from remote hosts, but it is not able to send them to another syslog server. This possibility will be implemented in 1.0.beta6 release.