It can be done. I have just gone through this, though a number of postings in these forums have stated that re-downloading audiobooks and movies is not allowed. I have been unable to find any explicit statement that it is Apple's policy to not allow thsi, but indeed audiobooks and movies are not included in the format for downloading past purchases. If someone can cite the actual rule for me, I'd appreciate it.
But it took the help and cooperation of Apple Support for me to get my audiobook back, and I feel they deserve substantial credit for it.
I can't promise this will work for everyone, but there's no harm in giving it a try. I first located my purchase history in iTunes on my computer and copied down the order number, date of order, etc. It was not, however listed in the new "purchased" list on iTunes. Then I checked to see if the audiobook was still available in iTunes and tried downloading it, and got the notice that I had already purchased it, and would be charged if I downloaded it again. I then contacted Customer Support for iTunes and stated my problem. The first response outlined all the steps for re-downloading purchases (which I had already done). The Apple email included a qualifier that the item I was trying to download might not be available on iTunes any longer or that it might be in a different format, thus making it unavailable. I had already made sure that it was still available, that Apple acknowledged that I had already downloaded it, it was the same price, etc., and that I believed my request was a reasonable one.
Today I received a reply telling me that the audiobook in question had been "restored" to my account (weird, since it was never lost), and that I could now download it if I opened iTunes and checked for "available downloads". Worked like a charm and I have my audiobook back.
Throughout Apple's tone was quite helpful and even conciliatory. At no time did they state that previously purchased audiobooks or movies are not available to be re-downloaded, just the question of a possible format change or an item having been deleted from the iTunes inventory.
I thanked Support for their assistance and then cited reports in these Forums that Apple policy was to not allow re-downloading audiobooks and movies; and I expressed my opinion that if, indeed this is Apple's policy, it made no sense and furthermore that it would behoove Apple to reconsider as a means of improving customer satisfaction. Who knows, maybe it will help? Certainly if everyone with this problem protests, it stands a chance of happening.
So give it a try! Just be sure to be polite but firm, have all your documentation in hand, and maybe you'll get that lost item back.
BTW, I am normally compulsive about backing things up, somehow this one book got lost. I have multiple iOS devices and a separate iTunes file for each. I now have one iTunes file I open when I want to purchase from iTunes, then import it to any other folder for the device(s) I want to use the purchases on. Thus I have only one file I need to keep backing up for iTunes purchases. I also now purchase most audiobooks through a membership in Audible.com, where they keep an archive from which you can re-download easily.
I hope this helps someone else with the same problem!