Hi Gagag,
Ok, so it sounds like you are using ArcGIS Server 10.1 with Portal for ArcGIS (which release?) and it is NOT a federated deployment.
Q1. What is the security/authentication model set for the Server site? This could be the built-in identity store, enterprise identity store, etc. Help topic here,
Configuring ArcGIS Server security—Documentation (10.4) | ArcGIS for Server
You can check by logging into ArcGIS Server Manager > Security tab.
Q2. Did you enable HTTP, HTTP and HTTPS, or HTTPS only for your Server site?
Secure ArcGIS Server communication—Documentation (10.4) | ArcGIS for Server
Q3. Did you set security on your web services from ArcGIS Server?
Restricting access to GIS web services—Documentation (10.4) | ArcGIS for Server
Q4. When you added your web services to Portal by registering them - did you specify the fully qualified domain name as part of the URL that you added? If they were secure, did you save the credentials with the item?
Add items—Portal for ArcGIS (10.4.1) | ArcGIS for Server
> Can you get the other end users to install Fiddler or Firebug to monitor the network traffic when they attempt to load the web app?
- Can't do this - IT won't allow.
That's unfortunate, because without this logged network traffic info, it will be challenging to help you troubleshoot your issue.