I'm not sure whether there is something in the console that does this, but it would pretty easy to setup as a scheduled job inside of windows on the server. Just create a batch file that archive's your logs and then deletes them. That way you have the logs since the last time the job runs.
The batch file would look something like this:
del c:\Windows\temp\SEP_INST.LOG.back
del c:\Program Files\Symantec\Symantec Endpoint Protection Manager\db\sem5.log.back
del c:\Program Files\Symantec\Symantec Endpoint Protection Manager\tomcat\logs\SesmLu.log.back
del c:\Program Files\Symantec\Symantec Endpoint Protection Manager\tomcat\logs\SesmLu-1.log.back
del c:\Program Files\Symantec\Symantec Endpoint Protection Manager\tomcat\logs\SesmLu-2.log.back
ren c:\Windows\temp\SEP_INST.LOG c:\Windows\temp\SEP_INST.LOG.Back
ren c:\Program Files\Symantec\Symantec Endpoint Protection Manager\db\sem5.log c:\Program Files\Symantec\Symantec Endpoint Protection Manager\db\sem5.log.back
ren c:\Program Files\Symantec\Symantec Endpoint Protection Manager\tomcat\logs\SesmLu.log c:\Program Files\Symantec\Symantec Endpoint Protection Manager\tomcat\logs\SesmLu.log.back
ren c:\Program Files\Symantec\Symantec Endpoint Protection Manager\tomcat\logs\SesmLu-1.log c:\Program Files\Symantec\Symantec Endpoint Protection Manager\tomcat\logs\SesmLu-1.log.back
ren c:\Program Files\Symantec\Symantec Endpoint Protection Manager\tomcat\logs\SesmLu-2.log c:\Program Files\Symantec\Symantec Endpoint Protection Manager\tomcat\logs\SesmLu-2.log.back