Audible.com is one of my favorite services - I have been a member for a decade, and have over 500 audio books from them.
However, there’s an inexcusable bug in the current version of their app. It’s inexcusable not only because it completely denies the user access to the app, but because it exists solely because they are harassing the user begging for reviews. Well, be careful what you wish for.
UPDATE: A friend of mine from Amazon indicated that an update has already been uploaded to the app store and is awaiting review. Glad I could help!