As you may have guessed, the KVM timeout value is not settable via MEBx / BIOS.
RealVNC should be able to set these. I'm not sure why it didn't work when you set AmtSessionTimeout to 0.
Try this: download and install Manageability Commander from http://software.intel.com/en-us/articles/manageability-developer-tool-kit/
Then you can add your DQ67EP by it's IP, enter credentials, and connect. Under the remote control tab, click the * next to KVM Remote Control settings. Here you can adjust the TCP Session Timeout. When you click OK, the settings are saved into AMT. Now, try RealVNC again. Hopefully it will not timeout. Let me know how it goes.
Thanks for the info. Im not exactly sure what fixed it. But I also ended up updating the Bios to 0055 (which I noticed just showed up for this board). I initially looked 1week ago, but looks like this Bios is brand new, just a few days old. So I flashed the new one, loaded defaults, and reconfigured the Bios to my liking.
Then I also installed that toolkit and set the Remote Control options as you said, except the timeout was already 0, so I set it to 1, and then back to 0 to make sure.
Now RealVNC been going to at least 30mins without that window in the foreground, its in the background and still there and not disconnected.