Downloading (using iOS or computer) past purchases from the App Store, iBookstore, and iTunes Store - http://support.apple.com/kb/ht2519 - enabled with iTunes 10.3 and newer; not all media formats are available in all countries (see: iTunes in the Cloud, iTunes Match, and iTunes Radio availability by country - http://support.apple.com/kb/HT5085); apps, books (not audiobooks), music, t.v. shows, and movies (some - not all studios have permitted this). Downloading previously purchased movies and TV shows requires iTunes 10.6 or later. Discontinued items not available. For items not included in the iCloud list (e.g., ringtones, audiobooks), or locations or computer systems where iCloud is not (yet?) available, you only get one download per fee paid. Apple recommends, "You always back up your iTunes library in the event that a purchased item is no longer available on the iTunes Store," (http://support.apple.com/kb/ht2519).
You may need to delete the entry completely from the library first before re-downloading or it will think the file is still on your computer.