I don't think it has anything to do with age.
If you want to go back to Windows 7, there is an easier way.
From within Windows 10, you can downgrade and restore the old system during30 days from the point of installation. Try to see if that works. You won't have to fiddle with JAWS activations, and your authorisation number should be retained.
And no, you cannot put the authorisation back onto the FS server.
And here's a tip for anyone wanting to spare the hastle when reinstalling.
Provided your machine stays the same and does not change its locking code after a reinstall, you can always authorise JAWS by putting JAWS.cps back onto the drive.
This file can be found in c:\program Files\Freedom Scientific\Activator.
Copy that to a save place, and whenever you have to reinstall your OS, copy it back to the same place.
You will not have to reauthorise, provided the locking code of the machine hasn't changed.