We are in the progresses of migrating a an application from
development into production and there are several web services that we
have built. When we access the web services this is the error message
that we are getting.

"The underlying connection was closed: The remote name could not be
resolved."

I can access both of the custom web services through IE.

I know of this article "PRB: Error on .NET client that consumes a Web
service through an HTTP proxy server". We are not using a Proxy
Server.