AD domain member DNS record randomly disappearing from AD’s DNS server

Sorry, I forgot to put in the question that these are static IP's. I realize I could add the DNS entries on the Windows side manually as well, but I'm not actually in charge of that Windows DNS server.

If you don’t have control of the DNS server, and if the DNS isn’t set up to allow non-secure updates, and it isn't set up to update based on DHCP assignments, and you have a static address, then you are probably out of luck.

Since this system has a static address, is there some reason you can’t just contact the person who runs the DNS server and ask them to add a record for your system?

There isn't a group policy setting to do what you're trying to do-- you're going to have to use a script.

First, I'd recommend reviewing the "Explain" tab for the settings you described above. You'll see that none of the settings actually turn on the registration behaviour you're looking for.

Assuming your machines get DNS settings from DHCP, and assuming that you don't mind this setting set back to the stock setting on all their network interfaces, assign the following in a Startup Script to the affected computers:

for /f "usebackq tokens=3* delims= " %%i in (`netsh interface ip show dns ^| find "Configuration for interface"`) do netsh interface ip set dns name=%%j source=dhcp primary

That will set the DNS client to get its address from DHCP, and reset the stock registration setting on all network interfaces on a Windows XP machine.

(An aside: You ought to figure out how your users changed that setting in the first place and stop them. It sounds like you have people who have 'Administrator' rights who shouldn't.)