Dbax and others, hope this will work for you too (suffered the same issue, tried different suggested ways, no result).
Purchased items should show up in your iCloud definitely!
This is on Windows 7 PC (maybe also works on Mac mutatis mutandis)
Apple puts your purchases from the store in your iCloud. And normally in your iTunes Library on your device as well. In iTunes Music section from the menu I turned [View>Show Music in the Cloud] OFF long ago because I got mad from all the double songs in my lists (1 copy on my PC (iTunes Library) and 1 in the iCloud).
Since the Store says "purchased", I suspected the songs actually missing on my PC (in my iTunes Library) to be present in the iCloud, I - temporarily - turned [View>Show Music in the Cloud] ON. And there the 'missing' songs showed up!
From the iCloud one can easily download songs to the iTunes library on your PC (right mouse > download).
I'm still wondering why 6 out of 8 songs smoothly downloaded into my iTunes Library (as expected) and 2 did not, but this is a way to get to your songs anyhow.
Why is this not indexed in Apple FAQ?
Cheers, Jeromy