I have the same problem only when connecting to vSphere Web Client from the outside.
When opening the VM console from the vSphere Web Client, new window tab is opened but after few seconds connection time out is received.
I then checked the client machine network connections and netstat showed that the client was trying to access vcenter internal LAN IP with port 443 with status SYN_SENT.
So the problem in my environment is that the console is redirected to an internal ip which the public user cannot access.
Maby somebody has any thoughts?