If the TCP query port is for some reason not reachable then only TCP query port based scripts like the TSViewer do have problems. People are still able to connect with the TeamSpeak client to a server and are able to talk with their buddies on it, the client does communicate over the UDP port.
Most common reasons for a not reachable TCP query port
- blocked by server firewall or not forwarded correctly
- TCP query port got changed
If you are hosting yourself then checkout the server configuration and your network settings.