On one instance of Portal we have running when you add a secure service from AGOL the options for saving credentials as seen below do not appear
In this case the Username and Password text boxes show up, but not the radio buttons. This basically breaks the ability to use the map with Collector. I have no idea what could be different on this Portal configuration than the others. Is there anything in the computer security that could cause this?
Has anyone ever seen this behavior before?
So the secure services is hosted on ArcGIS Online, as a hosted service? If you were to run Fiddler or the Dev tools while adding the service, do you see a checkURL request? Take a look at the response and see if it can successfully connect to the service. If not, take a look at the Portal logs to determine if there's a trust issue with certificates, (unlikely if the service is actually hosted on ArcGIS Online), or if there's simply a connection issue. If your Portal doesn't have the ability to make outbound connections, (in this case, to test the accessibility of the service you're trying to add), you may run into issues.
We too had this issue. We solved it by entering forward proxy settings into /arcgis/portaladmin/system/properties as documented at http://server.arcgis.com/en/portal/latest/administer/windows/using-a-forward-proxy-server-with-porta... We've had other issues since, but this got us part of the way there... Hope that helps.