You might need to provide more details (are you getting any error messages? Are you manually managing you iPod's music or automatically?) but here's the best place to look:
Connect your iPod to your computer, fire up iTunes and click your nano's icon on the left of the iTunes window. Look for the podcasts tab and make sure the sync Podcasts and 'automatically sync podcast' tick boxes are selected.
There's a really clear step-by-step here.
I have an alternative take on this problem:
I have just bought a Classic 160 Gb at Amazon few weeks ago and I have been facing the same issues as you.
I do not use Mac OS X, nor iTunes to sync. I run Linux and I use Media Monkey on a Windows VirtualBox Machine.
During the past two weeks I have tried everything that I could find. iTunes have not even been able to read my entire collection (strange, right?)
My findings
I have just restored the iPod firmware a few minutes ago. Started MediaMonkey and sync'd 10 songs from an ordinary random artist. Disconnected and the songs were there, nice. So the iPod is actually working. So far, so good, I have figured that out before.
However, in the meantime, while I was checking my library, I recalled that I have some songs from Japanese bands with Japanese characters in their names. Historically, this would be very error prone. So I did gave it a try, and sync'd 64 songs from that band. Disconnected the iPod and the songs were all gone.
So apparently the 2.0.4 firmware does not handle these characters very well. Check your library, make smaller tests. I am about to restore the iPod again and will try to sync some more files with normal ASCII characters. Will update you.
My old, now dead (waiting for a new disk), iPod, running 1.0.2 was able to hold those files nicely.
Best Answer
You seem to have done everything you can before resorting to really trying to restore it (which will wipe it). Bear in mind that an Apple store will probably wipe it or (if under warranty) replace it.