Since Apple has been selling audiobooks, which are provided by Audible, they have not allowed re-downloads of these books. I have long recommended to users to not purchase audiobooks from the iTunes Store for this reason. One hard disk problem, one iOS device crash, and you lose all your expensive content. Audible, on the other hand, has always allowed you to re-download your books from your library on their website.
This has now changed. 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.
The problem with this is that you’ll need to remember all the audiobooks you’ve purchased. I don’t know why Apple is making this so complicated; perhaps audiobooks will show up in your Purchased list in the near future. But it’s good to know that you’re no longer limited with this type of purchase, and, as such, I strongly recommend that users compare prices between Audible and the iTunes Store in the future (unless you’re an Audible subscriber, in which case books will almost always be cheaper from Audible).
This is going to change in iOS 9.3. The iBooks app in the current iOS 9.3 beta shows, when you tap Purchased, three sections: Updates (for updated books that you can download), Books, and Audiobooks. When you tap Audiobooks, you see a list of your books, with All Books, Recent Purchases, then a list of genres.
I expect that the next version of iTunes will also display audiobooks on your Purchased list, and allow you to view them the same way as on iOS.
If you’re not an Audible subscriber, you can get two free books if you sign up for a 30-day trial.