Thanks for visiting Apple Support Communities.
It sounds like you are streaming your matched songs from iCloud. As you've found, you can only sync music from your computer's iTunes library to your iPod.
With iTunes Match, you can download songs to your computer in addition to streaming them, as mentioned here:
iTunes 11 for Mac: Access all your music anytime, anywhere with iTunes Match
- To download the song, click the Download button.
Once downloaded, you can sync them to your iPod.
You may also want to use the "transfer purchases" feature to move songs from your iPod to your library, instead of downloading them individually from iCloud:
iTunes Store: Transferring purchases from your iOS device or iPod to a computer
Additionally, it's a good idea to back up your iTunes library separately. See this article for more information:
iTunes: Back up your iTunes library by copying to an external hard drive
All the best,