On the iPhone page of iTunes, I changed my backup from "Back up to iCloud" to "Back up to this computer". Then I clicked on the iTunes store and used the Purchased link. I found my music under "Recent Purchases" and where they had been shown as "Downloaded" before, they were now downloadable. Problem solved.
It seems like the iCould backup causes problems if used outside the US, so I guess I'll avoid it. Hopefully this helps you out if you haven't fixed the issue already.
jimmy2775, thanks for the info. Unfortunately, that didn't work for me. I already had iTunes backup set to "Backup to this computer".
However, I was finally able to download the songs, but not through an iPhone sync. Instead, I downloaded them via iCloud. I went into the iTunes Store and went to my account page (selected Account under my email address). From there, I went to the "Purchase History" section and clicked on the "See All" link. At that point, I clicked on the little arrow and was able to download individual songs or the entire album.
This doesn't really solve why I can't sync them from my iPhone, but at least I was able to get them onto my computer. Hope that helps.