This page details the issue:

http://blogs.msdn.com/b/lucascan/archive/2007/08/16/net-2-0-webexception-the-underlying-connection-was-closed-a-connection-that-was-expected-to-be-kept-alive-was-closed-by-the-server.aspx

It confirms that it happens on Web Service calls. This is exactly our situation. However, it says that this should be fixed in 3.5. We are at 4.0 now. There is a hotfix at the bottom. So, it is not clear if we should apply the hotfix or not, if we still have the situation under 4.0. But, it does say that this is a known issue, or was at least up until 2.0.