It turns out that what MATLAB is returning for the connection is ice.net.HttpURLConnection, which doesn't complete the connection, while sun.net.www.protocol.http.HttpURLConnection will. Adding the following fixed the Connect timeout problem:
% This version is needed on Windows 7 handler = sun.net.www.protocol.http.Handler;
my_url = java.net.URL([],site_name,handler);
% This version works on Windows XP, but won't work on Windows 7
% my_url=java.net.URL(site_name);