Hi Ben,
As Ajinkya highlighted the issue we faced was related to DHCP/DNS (name reslotion).
The issue came in with the hostname of the workstation from where PCO (Data Server) was running from at the time did not match the hostname entry in our DHCP database on the Domain Controller - so in short the DNS (name resolution) did not work and the hostname was pointing to a different workstation (IP) on the network.
The best way to see if the issue you face is the same – you could revert hostname in your connections settings to IP addresses and see if you are able to access the same and then work closely with your network team to resolve any name resolution issues to revert back to hostnames.
I hope this info will help you to resolve the same.
Regards,
Neil