I had some trouble with that too. It had to do with a setting in my iTunes. I wish I could remember exactly what setting, but I can't. You might go to iTunes>Help>Run Diagnostics if you haven't already.
Apparently it's a problem known to Amazon and they're "working on it." Someone suggested in another forum right clicking on the song and changing it to an MP3. The downside is that you end up with two copies of the song in iTunes, but I suppose you could delete the bad Amazon music file and keep the MP3.
An addendum to post above--right clicking and selecting AAC or MP3 doesnt work, at least with the two albums I've purchased from Amazon since the last iTunes update. I had to rebuy them in iTunes to get them to load onto my iPod. So buyer beware.
I don't think it's an iPod or iTunes problem. I bought an album from Amazon in MP3 format because it wasn't available as a CD. I tried to sync it to my Creative Zen through Windows Media Player but it won't sync. Anything that I rip from CD will sync fine, but for some reason anything that I download from Amazon won't sync. I won't be buying anything else in this format from Amazon.
I am just figuring this out after purchasing many songs from Amazon - looks like Apple want's to force us to itunes - I am disgusted. I will Not be using Itunes at all I will be switching my iphone back to a droid. Please stand up to Apple.