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.
After much experimenting and puzzling trial and error, I have found one thing that works for me every time -- create a playlist in ITunes for the music from Amazon you want to sync (and move the music into it, of course). For whatever reason, it will sync as long as the songs are in a playlist. Pretty simple workaround, really. I do hope Amazon or ITunes work toward a seamless solution, though.
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.