A lot of people have been having this problem with their ereaders (not just Kindle).
You have been hit with the curse of the Windows 10 upgrade.
Windows is not reporting your device as a removable device (Windows Explorer may know, but it isn't telling calibre

).
This has only happened with people who did an in-place upgrade to Windows 10 -- no one who did a fresh Windows install or started with Windows 10 has reported the problem.
So doing a fresh reinstall of Windows and reinstalling all your software *should* fix it, although that is a PITA.
Moderator Notice
This is a calibre problem, not intrinsic to the Kindle, so I am moving this to the calibre forums.