Not necessarily ArcInfo/advanced, we just happen to have that version installed on the old VM, you cannot use a version of ArcGIS Desktop newer than 10.0 to access ArcGIS Server 10.0 via an administrative connection. Below is the reference from https://resources.arcgis.com/en/help/.
We found that note in the 10.1 or 10.2 documentation. Using 10.8.1 we are able to make "user" connections to the ArcGIS Server but cannot create "publish" or "administrator" connections via ArcCatalog. We also installed a copy of ArcGIS Desktop 10.2 and tried that as well, with the same results. The credentials we are using are able to log onto the ArcGIS Server Manager web interface and works with the "user" connection, so it should not be a permissions issue. The tools we would like to run against the server are not available with just a "user" logon. It needs to be an "administrator" logon.
The connection error we are getting is noted below which made us question the URL and the reason for our original post. After finding the archived help documents, we believe we are using the correct URLs to connect and the issue is most likely newer versions of ArcGIS Desktop cannot be used.
Your post made me question if we had interpreted the ESRI's note correctly, so I went down that rabbit hole again. Unfortunately, we found the same information but this time without question. Only ArcGIS Desktop 10.0 can be used to manage ArcGIS Server 10.0.
This is from - ArcGIS Help 10.2, 10.2.1, and 10.2.2 as was the previous note found in another section.
