Can't read Comixology comics purchased on my Kindle Fire since app update

Since the Comixology Android app update a few days ago, I've been unable to read any comics that I had previously purchased on my Kindle Fire. The app tells me that the device is not authorized to read these comics. I'm directed to sign in, but I'm already signed in on that device with my Comixology account. I saw on their Facebook page that they have some work-arounds to try, but they don't list them anywhere on their site. How can I read comics in the updated Comixology app that I had purchased before the update?