How are you pausing it? The onscreen controls, headset, or other?
If onscreen, then I don't know. Still.
If you are using the headset, and it only happens with Audible, then it's probably a glitch with the Audible app. The Music app will start playing when you push the pause/play button on the headset, unless some other audio app is loaded. That app normally takes the controls away from Music.
I don't have Audible, so I can't test it. I do have Pandora and a few other Music apps, and they work as expected.
So test a bit more, and see if it's just Audible. If it is, I'd recommend contacting their support and seeing if they have a solution. My solution would be to delete and reinstall the app, but I'm not familiar with how you'd recover your audiobooks afterwards, so I think it best you talk to them; or someoner her who has the app and is more familiar with it.
Yes, I'm backing off the hardware idea. After more consideration it just doesn't fit.
If it's more than just the Audible app, then it's more likely a system wide glitch. I'd recommend trying to Reset All Settings. After that, you're probably looking at a restore; which needs some preparation if you don't want to lose content.
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Reset All Settings: Another, somewhat more drastic thing you can do is Reset All Settings. You'll find this under Settings > General > Reset > Reset All Settings. It won't erase any of your content, apps, or accounts; but you will have to go through most of your other settings and re-tweak them back to your liking.