I have seen this issue before but just as @BenFB noted it always turned out to be firewall issues.
As a test from the machine having the issue run telnet and try to connect to <server address>:4172 if it never connects you have a firewal issue and :4172 (PCoIP) is not open on the server you are trying to connect to. If you have the servers behind a loadbalancer I would remove one server at a time out of the load balancer and test all of them.
By any chance is this happening only when tethering to a hotspot like a mobile device for something? I have seen some issues with connectivity from mobile hotspots that use Multi Source Proxying were the ISP (AT&T in the case I know of) splits the traffic based on ports to various proxy servers to parse out the traffic. So :80, :443 might go through one Proxy Server but your :4172 might go through a different proxy server. Normally the traffic should converge back together at the destination but the load balancer was thinking the traffic came from different sources so it wouldn't always send the customer back to the same security server they authenticated to for the 4172 traffic. When this happens the security server you did not authenticate to will see you try to pass 4172 traffic and drop you because you didn't authenticate with it. To test for this try to logon when it fails take a look at the logs on your external connection brokers (the ones paired with your security servers) and look for the session information. it should only be on the one you connected to for authentication.
