It sounds like you are trying to dwonload an audio book purchase from iTunes but the download is stopping on its own. I would start by quitting your open apps on the phone.
iOS: Force an app to close
Double-click the Home button.
Swipe left or right until you have located the app you wish to close.
Swipe the app up to close it.
When you have done that, sign out of your iTunes account in Settings > iTunes and App stores, and restart the phone, sign back in and try the download again.
iOS: Turning off and on (restarting) and resetting
If the issue persists, I would next backup your device to iTunes, and restore it:
iOS: How to back up and restore your content
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