On my 925 with tmobile the app worked ok. It always played, sometimes would loose my place, but it was bearable.
On my new 1520 with at and t I am having the "stuck in pause" trouble like others in this thread. This is a reply from audible.com
"Thank you for contacting Audible. My name is Yilme and I hope you are having a great day.
I understand that you would like to know If the Audible app will be updated to fix ongoing issues.
I am sorry about the inconvenience that this has caused you but I am more than happy to assist you with this.
I do not know when there is going to be an update for the Audible for windows app.
The Audible app for Windows phone was last updated on November 26,2013 by Microsoft, only the Audible for android and iOS for iPhone/iPad is controlled by us directly.
We are aware that there is stability issues the Audible for windows and is working with Microsoft to have it resolved."