Google has made known that it is in the process of figuring out exactly how to handle the device authorization and de-authorization for Google Music, and for the time being they have reverted to the old method allowing unlimited device de-authorization. From Google Play's help pages:
Yesterday we made a change to our device policy for music on Google Play. Any user can associate up to 10 devices to his or her account. Once you have connected 10 devices, you may add a new device only by deauthorizing an existing one from your account, and you may do this up to four times per year.
We limit the number of times you can swap out new devices at the request of some of our music partners in an effort to limit abuse. We understand this has caused some issues for users who often deauthorize and reauthorize the same device, and we are currently re-implementing the solution in a way that works for our users and music partners.
We apologize for any inconvenience and will update this page as new changes are made.
We're not sure how they plan to address the issue, but we're sure glad they have given us all a chance to clear out all our old devices. Hopefully they can implement a fix that doesn't add the same device multiple times, but that still won't be a solution for folks who need to switch devices often. It's an interesting dilemma, and one that hits close to home. We'll keep our eyes on this one.