A possible reason for what you describe is that you have (in the past) used more than one Apple ID to make purchases. The Apple ID you currently use may not be the Apple ID you previously used to purchase some of your songs.
Find one of the purchased songs that does not sync to the iPod in your iTunes music library and select it. Right-click and select Get Info. On the Info window's Summary tab, find where is says Apple ID. If that is a song purchased from the iTunes Store, the Apple ID used for the purchase is shown there. Is that your current Apple ID (or a different one)?
If it's a different one, from the menu bar, under Store, select Authorize This Computer. In the window that comes up, where it says Apple ID, enter that other Apple ID (not your current one). Enter the password for that Apple ID. Click Authorize. NOTE: One computer can be authorized with more than one Apple ID, so the authorization for your current Apple ID is still valid. It's now authorized for BOTH Apple IDs.
The songs that do not transfer should now transfer. If some still do not transfer, perhaps you have another Apple ID that was previously used for purchases from the iTunes Store. If so, repeat this process...
NOTE: For songs, this problem should only affect older purchases that use DRM (copy protection). More recent song purchases from the iTunes Store no longer use DRM, although purchased videos (movies, TV shows, and music videos) still use DRM.