DNS server settings don't survive a reboot

Please attach the following files to this bug:
/etc/network/interfaces
/etc/resolv.conf

You should do this immediately after the boot (before changing settings manually again)

Well, please note that I have now manually modified my /etc/network/interfaces to make the settings "stick" (by adding a "dns-nameservers" entry manually).

However, I will restore the file to the status it was originally after my Kubuntu installation, and the proceed as you suggested.

These are my resolv.conf and interfaces files as they originally looked.
As I mentioned, I have later modified interfaces manually to add a "dns-nameservers" entry, but I'm pretty sure this version I'm uploading has those changes properly reverted.

These are my resolv.conf and interfaces files after setting a DNS server in KDE's control panel applet (like described in the bug report), but *before* a system reboot.
(Note that I have not set a domain name here, only a DNS server; however, adding a domain name, too, behaves similarly).

These are my resolv.conf and interfaces files as they appear after setting a DNS in KDE's control panel applet, and after the system has been rebooted.

Your /etc/resolv.conf has this comment:
# Dynamic resolv.conf(5) file for glibc resolver(3) generated by resolvconf(8)
# DO NOT EDIT THIS FILE BY HAND -- YOUR CHANGES WILL BE OVERWRITTEN

Do you have resolveconf package installed from universe?
http://packages.ubuntu.com/dapper/net/resolvconf

Can you try removing this package and see if it helps?

Yes, I had that package installed (I believe it is a standard Kubuntu package), and removing it helped.
Now KDE's settings seems to stick in /etc/resolv.conf.
I suppose that either resolvconf should be removed from the default Kubuntu packages, or the KDE Network settings should be made to modify /etc/network/interfaces rather than /etc/resolv.conf - does that sound right?

resolvconf package is for sure not part of standard Kubuntu install as it is in universe repository (and stuff from universe are never installed by default).

The only other package mentioning resolvconf is avahi-dnsconfd, which lists it as Recommends - it is possible that you got this package installed as by aptitude which by default installs Recommended packages.
Did you install avahi-dnsconfd.

I think we can close this bug as Rejected (unless somebody thinks that Recomends has to be changed).

I suppose you can close the bug, though I have no idea where resolvconf could have come from if it's not a default package (no, I don't have avahi-dnsconfd installed).

Actually, I think it might have come from postfix, which lists it as a Recommended, and which I think was installed by some program I installed right after my Kubuntu was set up (but I later removed that program, whatever it was).

If my recalling of this is correct, though, I don't see why resolvconf has been kept installed: if I used aptitude, it should have removed it when removing the other package, and if I used apt-get get, it shouldn't have installed it at all since it's just a recommend.