Checking the Event Logs, I found two events which showed the following:
My next step was to check the health of WSUS with the following command:
WsusUtil.exe checkhealth
This was run from "C:\Program Files\Update Services\Tools" directory
Running this command gave me the following result:
1. Install the HTTP Activation role under .NET Framework 4.5 Features through Server Manager.
2. Restart the WSUS service
Yep...it was that easy! After doing that, adding the WSUS server back into the MMC console worked fine and everything was back up and running again.