Jul 27, 2015 · An existing connection was forcibly closed by the remote host 0 0 WEBSITENAME We've been troubleshooting these since DAYS [Not hours] - We've read all following blogs/articles. Tried all possible solution.
Since you say you're using ArcGIS Desktop 10.5.1, here is some information on this product: Products Affected by TLS 1.2 Implementation; How To: Install the TLS 1.2 patch on ArcGIS Desktop In regards to the second link, you'll be directed here, which is the downloadable ArcGIS Desktop TLS Patch. Make sure ArcMap is closed and download the above patch, after that try to add the basemap to ArcMap again. The underlying connection was closed: An unexpected error occurred on a send of web request1