Suggestions and a comment....
ALWAYS check the stupid stuff first. That's a rule I try to live by (because when I don't and the answer is simply *I FEEL* stupid..lol)....
So then...check the health of the cable itself and the switch ports it plugs too (or patch panel, whatever your system is..actually check both the patch and the switch).
You are looking for obvious damage to anything, you are also looking for loose connections..lord knows some RJ-45 connectors in my time have not "connected" all that tight and they tend to come loose VERY easily.
Of course disabling and re-enabling the connection and that causes it to work again would limit the chance of a loose connection issue a bit. I'd still check it. Stranger things have happened.
Also how open is this system? By that I mean in two regards -- straight out security wise and are you the sole person who has rights/works on this machine?
Theories on this are -- possibly some virus infection causing instability, someone who is going into the system unbeknownst to you and fussing with things (we had a user here who swore up and down his lan conneciton would work some times and other times it wouldn't...after some talking with him and looking things over -- he was disabling the connection manually..he thought you had to turn it off as part of the computer).
Next move on to drivers (if you think its stupid well that's what I call it "Checking the Stupid things"). Perhaps nuking the current drivers, and then shutting down, re-boot and download and install the latest version ones fresh again.
The reason I'm saying this stuff is because we all know that DNS is a service, it shouldn't just shut down unless its configured to do so.
I'm making all assumptions that you have checked the service settings already, that you tried stopping--restarting it, and that DNS is properly configured.
The last stupid thing is did you install any new software recently or make any system changes within the sam