Kirk McElhearn with a nice find:
As of March 3, according to an Apple support document, you can re-download audiobooks. Unfortunately, the procedure isn’t simple. Instead of audiobooks showing up on your Purchased list, with all the other content you bought from the iTunes Store (with the exception of ringtones and alert tones), you have to manually search for each audiobook to be able to download it. On iOS devices, the procedure is the same. In the iBooks app, search for an audiobook, and you’ll be able to re-download it.
Apple Now Allows Re-Downloads of Audiobooks Purchased From the iTunes Store | Kirksville
That's pre-iOS 9.3 — as McElhearn goes on to explain, iOS 9.3 (I'm running the public beta) makes things much easier: from the iBooks app, go to Purchased (on the bottom navigation) → Audiobooks → All Books → Enjoy!