/var/log/Xorg.0.log permissions after reboot

I'm attempting to set persistent 0600 permissions on /var/log/Xorg.0.log, it seems that something is resetting them to 644 after each reboot.

I have tried putting the following line in /etc/rc.local

~~
chmod 0600 /var/log/Xorg.0.log
~~

The seemingly automated permissions change happens a few minutes after login thus negating the rc.local script.

Any help would be very much appreciated.

I'm running RHEL Server 6.9