Q: Can't download a audiobook that i purchased ?

Do you mean download or re-download ? If download then what happens when you try ?

If re-download then audiobooks are currently a one-time only download from the store, and they aren't included in iTunes Match, that's currently for music only. If you don't still have a copy of it on your computer nor on a backup of your downloads, then if it's still in the store you could try contacting iTunes Support and see if they will grant you a re-download : http://www.apple.com/support/itunes/contact/ - click on Contact iTunes Store Support on the right-hand side of the page, then Purchases, Billing & Redemption

I am having this issue on ios 7.0.3, with an audiobook I purchased.

My phone will NOT download the audiobook.  Music app shows the 3 tracks of the book, but there is no audio/no data - and the store app indicates the book has been "purchased" but does not actually download.

- have tried the 'safari cookies' change

- allowed downloads over cellular/4G connection

- have "deleted" the audiobook and tried to "re-purchase" but fails & simply adds the "name" of the audio book back to the music app, with NO CONTENT

- have restarted the phone

- have upgraded from 7.0.1 to .3, still same

- I cannot wipe the phone.  That is a ridiculous way to get to the download

Other content (music) downloads fine. 

Contact itunes support