Check in the IIS Manager to see what authentication type is enabled on the directories that are part of the WSUS Server. Windows Integrated Authentication needs to be enabled on the
"SimpleAuthWebService",
"Content",
"ClientWebService",
"ReportingWebService",
"SelfUpdate" folders.
After correcting this, all my clients are making successful connections and downloading approved updates, as well as reporting to the server that the client exists and is using the Windows Server Update Services server.