Your problem seems to occur at 23:59h, that's the time when ISPConfig stops Apache to process the logs and then starts it again. Maybe the problem is that Apache gets started too soon after it has been stopped. You can try to modify the start section of the init script like this:
[ -f /etc/apache2/httpd.conf ] || touch /etc/apache2/httpd.conf
#ssl_scache shouldn't be here if we're just starting up.
[ -f /var/run/apache2/ssl_scache ] && rm -f /var/run/apache2/*ssl_scache*
echo -n "Starting web server: Apache2"