The correct procedure is to move the logfile, then signal Apache to tell it to reopen the logfiles.
Apache is signaled using the SIGHUP (-1) signal. e.g.
mv access_log access_log.old
kill -1 `cat httpd.pid`
httpd.pid is a file containing the process id of the Apache httpd daemon, Apache saves this in the same directory as the log files.
(httpd.pid is in /var/run on plesk)