Windows Remote Desktop: "configuring remote session" closes without error

I started having a similar problem out of the blue on a PC at work--it connected and just hung there at the 'configuring remote session' window.

I found that I needed to go into the options under the 'Experience' tab and de-select the Persistent Bitmap Caching setting.

Once I disabled that setting I was able to connect quickly as expected.

This can also happen if you have initiated a large Windows Update that is not yet fully configured or if the computer is not yet fully restarted. You can not remote to the desktop but the IIS might still receive and return responses for example. In this case all you need to do is wait.

A good thing to try is also deleting %localappdata%\Microsoft\Terminal Server Client\Cache and restarting your computer as mentioned by @JohnLBevan in comments.