Cannot use VirtualKeyboard when using several modal Popup

See the attached example to reproduce the issue.
In the sample application, the keyboard works when only the first Popup is open. The keyboard is display in front of the Popup and can be use to type text in the TextField.

However, opening a second Popup via the button in the first one disable the keyboard. Even the close keyboard button is not working.
After closing this second Popup, the keyboard is still not working. It just works after all popups are closed.