After basic troubleshooting, I discovered that the Windows Firewall was blocking port 3389 from all sources, which was set by server.
I then confirmed that I could RDP to other servers in the same security groups and OUs.
I ran GPRESULT /R GPreport.html, which returned the following results.
Labtech is in use on this site, and the firewall rules are set from within the Default Domain Policy.
A quick look around advised me that this error for Windows 8/Server 2012 had this hotfix available. Windows 8.1/Server 2012 R2 has this issue fixed with this update
After installing this hotfix, and rebooting the server, I had one rather happy client.
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