There's no obvious reason why recording is not working as expected. When the login screen closes and a new window opens Test Studio is supposed to recognize the new window and automatically connect to it.
Your screen shots show Test Studio is trying to connect to it but for some unexplained reason the process fails with your application. Since this is a recording problem we need to be able to reproduce the problem on our local machine so we can investigate and determine what is causing it.
To that end, is there a publicly accessible URL we can connect to? If not our next best option is to get a Fiddler trace of your application running normally in a browser. We have about a 75% success rate using the Fiddler trace to simulate your web server and reproduce problems that way.