Screen readers often stop interacting with Skype since version 8.63
Since Skype 8.63, there is a screen reader bug present with all screen readers.
If you press alt f4, which will hide the app to the system tray, then restore it back by pressing enter on the Skype icon, the app won't respond to any keyboard command.
Pressing Tab, alt 1, nothing will work.
To get out of this inaccessible state, it is necessary to press alt once to focus the menu bar, then escape to close it. This will restore the keyboard navigation, until you perform the same operation again, that is, hide Skype back to the system tray and restore it, which will make the bug happen again.
Nikola Jović commented
as far as I am aware, 8.65 is still in preview and not officially released. However, after downloading the preview of the desktop app, I noticed that the issue can still be reproduced.
Thanks for sharing this feedback with us Nikola. Have you tried updating your Skype to version 8.65 on the Windows Store app or 8.64 on the web app? Please let us know if that resolves your issue.