After upgrading a vSphere vCenter appliance to v5.1 Update 2 we found the the vSphere client installed on a Windows XP or Windows Server 2003 host machine would fail to connect to the vCenter Server 5.1 due to an unknown error.

vSphere Client could not connect to {vcenter_server}.

An unknown connection error occurred.  (The request failed because of a connection failure. (Unable to connect to remote server)).

VMware posted a technote for vCenter 5.5 regarding the SSL connection that appears to also work with the vCenter 5.1 Update 2 

For the vCenter Server Appliance

We hope that this information is helpful. Please let us know how this has helped you or if you have additional questions. As always Firestone Technical Resources, Inc. is here to help with your computer support issues - "Providing personal service for your impersonal technology."