I don’t mean to hijack someone else’s issue, but I am having the same problem. I’m sure I was able to update one of my websites, but others are failing with this same unauthorised error. I am a bit confused by the information on the link you provided.
If that URL changes at any time, you need to re-authorize your license key or you’ll received an “unauthorized” error when trying to update.
The URL has not changed, but I do use GP Premium on a few sites (“Unlimited websites”) so I am not sure what I am supposed to do in this case. Do I need to re-authorise for every site (minus one) that I use GP Premium on?