Why can't I re download audio books?

As far as I know they are all supplied to Apple by audible.com, so I assume that it's them that are requiring the one-time only download rule (tones are also one-time only downloads ; other items are only redownloadable whilst they remain in your country's store and you don't move countries). If you no longer have them on your phone then sync them back from your iTunes library - if they aren't currently in your iTunes library then add them back from your backup of your downloads/library via File > Add To Library and then resync them