It is possible to have multiple servers connect to the same PortServer TS unit. You might want to confirm that you can ping the unit form the Windows PC. Additionally, please ensure the 771 port is not being blocked/firewalled as this is the port used by the driver for communication.
Lastly, you may need to enable port sharing in order to access the ports simultaneously. This is set in the web interface under Configuration > Serial Ports > (Port #) > Advanced Serial Settings > Allow multiple systems to simultaneously connect