Start with Basic things to pin point your issue.
First tell everyone here when this happens. And are you seeing a dialog box that says graphics drive reset?
Second check your bios version.

I don't see it being a psu problem with the issue you described. Any chance you still have your old gpu to throw back in and see if it will happen? Also have you tried loading default values again in bios? I know you said you are running stock clocks on everything but maybe a setting was changed.

What else could it be? I am still currently testing it with the 680. Nothing so far...but I haven't really been watching it.
I had a power surge detection with my mother board, where the PC just shut down and then when I rebooted it. It said that the motherboard detected a power surge. The problem with the display going out was happening prior, it just became more frequent.

MAC156
What kind of PSU are you using and how many watts? maybe check your pci-e power connectors to GPU and PSU.

SilverStone ST 1500W, I swapped out the 980 with a 680. It has been working without problems, it is the card I used previously on this build with no problems.

Vlada011
That's probably driver stop responding, you can check in event viewer when that happen you will have warning message.
If GTX680 work normal than PSU can't be problem because GTX980 need less power than GTX680 and GTX780...
Maybe is problematic driver... Did you have some errors or similar black screen in gaming demanding games?
If you had problem than probably card refuse to work on fabric OC.

It seems so, I get Event 4101, Display.
"Display driver nvlddmkm stopped responding and has successfully recovered."
 
It shows I got a lot of those...and all dates that I have been using the 980 Classified. 64 events in total. It happens at times one after another. It happens in game, when I tab out the game, or when the system is pretty much at idle and I am surfing a website or just clicking through icons. When it happens the card fans would sound like they stopped and light would flicker a little on the 980 Classified. That means it's a drivers issue then? How can I resolve that?

Try with some older driver. If you have CD from graphic card box you can install same version of driver or one of first 2-3 for GTX980.
Clean after uninstall with driver cleaner or some other software, clean registry, temp files, etc... and install new driver Clean Installation checked. Only Display Driver and PhysX... Avoid 3D and Experience until you see what cause problems.
If driver stop working continue, black screen in games you need to send card to EVGA as RMA and ask them to test new before send you.
You can check one more thing... Downclock your card with some software as Precision X on same clock as reference GTX980 and continue to use your card 2-3 days in different situation, benchmark tests, games, special in situation where you had problem with fabric clock.
If nothing happen and driver crash stop that will confirm unstable fabric clock too.

with new hardware bios will shutdown/restart to configure. Is this what you are speaking of?

Vlada011
Try with some older driver. If you have CD from graphic card box you can install same version of driver or one of first 2-3 for GTX980.
Clean after uninstall with driver cleaner or some other software, clean registry, temp files, etc... and install new driver Clean Installation checked. Only Display Driver and PhysX... Avoid 3D and Experience until you see what cause problems.
If driver stop working continue, black screen in games you need to send card to EVGA as RMA and ask them to test new before send you.
You can check one more thing... Downclock your card with some software as Precision X on same clock as reference GTX980 and continue to use your card 2-3 days in different situation, benchmark tests, games, special in situation where you had problem with fabric clock.
If nothing happen and driver crash stop that will confirm unstable fabric clock too.

What program would you suggest for cleaning registrar and rest? CCleaner?

kot0005
I had a similar TDR issue with my 980 classified. Had to RMA it. But you better do more tests before RMA
. These cards don't seem to be living up to expectations. Its looks like the class's are going to be regular ACX versions with beefy power supply. I think the kingpins are the new 'Real" Classified's. So sad.

I had planned to RMA it and even did the process, and last minute decided to just return it. Will wait for the Ti or possibly get the Titan X.
- After reading on newegg reviews people having similar issues with the EVGA 980 Classified.