You may have noticed that since upgrading to vSphere 5.5, the vSphere client gives you this error when trying to login from a Windows 2003 Server:

“An unknown connection error occurred. (The Client could not send a complete request to the server. (The underlying connection was closed: An unexpected error occurred on a send.”

This is a known issue and is caused by a lack of SSL ciphers on Server 2003 (and Windows XP). There is a fix, however, it only works on 64 bit versions of Server 2003. You can download the hotfix from Microsoft here:
http://support.microsoft.com/kb/948963