Comment 46 for bug 284298

On Ubuntu 10.04, I had a similar problem related to /etc/resolv.conf editting.

I checked #91890,
https://bugs.launchpad.net/ubuntu/+source/network-manager/+bug/91890

I found that someone already gave a nice solution for working around this weird problem as below:
Edit your /etc/resolv.conf for the nameservers you want.

And then

sudo chattr +i /etc/resolv.conf

The the resolv.conf is locked and no program could change it. If you want to change it back to be editable

sudo chattr -i /etc/resolv.conf

BTW, I found an dns checking script with the path of
/usr/lib/avahi/avahi-daemon-check-dns.sh

For those who might be interested, I pasted the script here:
https://photon.snipt.net/avahi-daemon-check-dnssh/