I am experiencing this problem also. I downloaded some TV shows recently that are missing artwork. I sent an email to iTunes Store Customer Support. The response I received suggested that I re-download the TV shows. If artwork is available for them, then it would be downloaded; if not, then there was nothing that could be done. This response is of little use and I intend to get a better one.
Here's what I've learned:
1) My downloads showed artwork while downloading. The artwork was replaced by the generic iTunes TV Show icon after the downloads were processed. When I select one of the downloads, the artwork viewer says, "Drag Artwork Here." When I select "Get Info" for one of the downloads, the artwork icon on the "Summary" tab says, "No Artwork Available" and the "Artwork" tab is disabled. I think the artwork was downloaded though because my "Album Artwork" folder has increased in size since these downloads.
2) The "Get Album Artwork" feature does nothing to resolve this problem. Re-downloading does nothing either.
3) I used Quick Look on the "iTunes Library Music.xml" file and did notice something. These downloads are missing the line "<key>Artwork Count</key><integer>1</integer>," which all of my other downloads with artwork have.
4) I tried removing the TV shows from iTunes and keeping the files; I then re-added them to iTunes. This created a new problem by iTunes adding them as Movies and removing all of their information from the "Get Info" tabs.
5) I'm only experiencing this with TV shows. Music and podcasts show artwork. I'm not sure about movies, books and apps. I've tried to recreate this problem on an iPad 2, an iPod touch (3rd Generation) and another MacBook Pro running MacOS 10.6.7 and iTunes 10.2.2. I think there may be an issue with iTunes 10.2.2 because my downloads from the day before I upgraded are okay. All of my downloads from after upgrading are not.
I also came across another discussion that seems related:
I store my library on network-attached storage. I haven't tried downloading to my internal hard drive, so I'm not sure if this is a cause.