DNS servers in /etc/resolv.conf change after a reboot/network service restart.
You would also see messages shown below in the /var/log/messages file:
Oct 10 12:40:52 hostname NET: /etc/sysconfig/network-scripts/ifdown-post : updated /etc/resolv.conf Oct 10 12:40:57 hostname NET: /etc/sysconfig/network-scripts/ifup-post : updated /etc/resolv.conf
How to make entries in /etc/resolv.conf permanent
1. The /etc/resolv.conf file will be overwritten if any network interfaces use DHCP for activation. To prevent this, ensure such interfaces have PEERDNS=no set in their ifcfg file, for example:
# cat /etc/sysconfig/network-scripts/ifcfg-eth0 TYPE=Ethernet DEVICE=eth0 BOOTPROTO=dhcp PEERDNS=no
2. The ifcfg-file directives DNS1 and DNS2 can also lead to modification of resolv.conf. To prevent this, either remove said directives or use chattr(1) to make resolv.conf immutable to changes, i.e.:
# chattr +i /etc/resolv.conf