Audible App plays 2 minutes of a book and then shuts down on my iPhone.

You can first check your Internet connection and try to restart the Audible app and your iPhone. If it does not work, try to update the app or reinstall it. Also, you should make sure that you don't open the low power mode and batter optimization. To fix Audible keeps stopping , you can also try to go to open Settings > General > Background App Refresh > Audible.

[Edited by Moderator]

See if a force close of the app and restart of phone helps. If not, you could either try offloading the audible app or deleting the audible book and redownloading.