Eu tive o mesmo problema há algum tempo, e foi porque o pacote resolvconf não foi instalado. tente instalá-lo usando
sudo apt-get install resolvconf
edite o arquivo resolvconf e reinicie a rede via
sudo /etc/init.d/networking restart
também como é o seu arquivo / etc / network / interfaces?
Eu também recebi uma dica dessa resposta em um tópico anterior semelhante ao seu. link
A possible trigger for the seemingly spontaneous updates to /etc/resolv.conf is when your DHCP lease is renewed. Check how long you get DHCP leases for (this should appear in the system logs, I think in /var/log/syslog).
You can use auditd to find out what modifies the file. Start the daemon (sudo service auditd start) and tell it to watch for modifications to that file:
sudo auditctl -w /etc/resolv.conf -p w
Audit logs are in/var/log/audit/audit.log. You'll see the time the file was modified and the name of the program that modified it.If you have the resolvconf package installed, Network Manager may be stepping on its toes. Try bringing all network interfaces down, then stop Network Manager (sudo service network-manager stop), then restart it.