I have been using Ubuntu Mate 21.04 since January with no problems until about 4 or 5 days ago. At that time DNS stopped. I've Googled and tried several "fixes" with no improvement, especially since the resolve system has changed almost yearly. The only thing that seems to work is to replace the "127.0.0.53" in /etc/resolv.conf to "9.9.9.9" or some other known resolver, which works until reboot. Reinstalling, including complete "nuke and pave", works for a few hours, then on a reboot it stops.
I've made a copy of the modified /etc/resolv.conf file and placed it in my home directory so when I reboot I can simply "sudo cp" it to /etc.
What am I running on? Thinkpad W530, Ubuntu Mate 21.04
I had left the DNS setup default yesterday, however the install script configured it. The default is AT&T DNS from the Pace 5268AC Uverse router, which works just fine with 5 other computers, 2 Rokus, and 2 Galaxy S9 phones. This afternoon I tried "Edit Connection" - 9.9.9.9 and 1.1.1.1 (with a comma in between, no spaces) in the DNS box, "Automatic, dhcp only" in the dropdown box. Still have to copy my custom /etc/resolv.conf from my home directory to /etc to get DNS to work.
It used to be you could set the resolv.conf and then mark the file "immutable", but they have taken that away from us. You also can't make /run/systemd/resolve/stub-resolv.conf immutable.