This was a recent issue discovered when new computers were installed. Shift key did not respond while using remote desktop from a Windows 10 computer to our Windows 2008 R2 Enterprise edition server.
-Open the Remote Desktop application
-Click down arrow at bottom left of application window "Show Options"
- Select "Local Resources" Tab
- Under "Keyboard" you'll see "Apply Windows key combinations"
- Select dropdown menu and change to "On this computer" and then you are done with this tab
- Select the General Tab
- Under "Connection settings" you have the options to select on of these buttons "Save, Save As..., Open..."
- Select the "Save" button
- You are finished, now test!
Note: if you select either of the other two options the shift key did not respond in my environment.
- "Only when using the full screen"
- "On the remote computer"
I hope this helps someone out :)