Hello Dixie,
Is the WMS service server on a different network than your Enterprise Deployment? It's possible that the requests made by Portal to the service are being blocked. If that is the case you may need to work with your IT Department to allow access to the WMS service. Outside of portal your network configuration may limit access to resources from outside your internal network. Commonly this might be a firewall or reverse proxy.
I would recommend logging into the portal machine under the portal Windows service account. Then try and access the WMS service in a browser. Again if this fails the requests may be being blocked. I've also added some steps below which should help capture additional traffic using Fiddler.
Enable Fiddler to view 'HTTPS' traffic:
1). Open Fiddler > Tools > Options.
2). Navigate to the 'HTTPS' tab in the Options window.
3). Check 'Capture HTTPS CONNECTs' and 'Decrypt HTTPS traffic'
4). After clicking 'Decrypt HTTPS traffic' you should be prompted to trust the Fiddler root certificate.
5). Click yes through the follow prompts.
If you have the option you may want to create a case with support. They would be able to assist further with troubleshooting the WMS service issues. If you have any additional questions please let me know.
I hope this helps!
Thanks,
Thomas.