If the auth is machine specific, it shouldn't matter if you restore, re-install windows, update, etc. .. the machine should use only one authorization.
It should keep track of this type of adjustment to the system.
That said, I do admit to keeping a notepad file of critical keys and also saving a backup of that file to an external storage .. be it thumb drive or 'cloud' storage (or both).

I do not work here, but the benefits are still awesome
Make your sound your own!