You need to play at least a part of songs purchased from the iTMS to authorize them. They won't copy to your iPod until you do this.
How to transfer Purchased Music from iTunes to your iPod
iTMS Song and Computer Authorization
If you've played & authorized them in iTunes and they still skip, try this. De-authorize the computer in iTunes/Advanced menu, then re-authorize it. You re-authorize it by playing one of the songs purchased from the iTunes Music Store within iTunes. It should ask you for your Apple ID and password, and then the computer will be authorized again. Sync your iPod with iTunes, and those songs should play on the iPod once again.
Another common cause of this is not having the latest version of iTunes.
If you are using the latest version of iTunes (6.0.2), then you need to make sure your iPod software is up to date also. Get the
iPod Updater software, install it, run it and update your iPod.
When you have done this, authorize your music in iTunes by playing a few seconds of it within iTunes, re-sync your iPod, and it should transfer by whatever synching method you choose.
