It has nothing to do with being authorised, that doesn't affect Podcasts. Plus, you already have them on your computer.
Did you have to change the settings for the Sync Podcasts? If you did, then you may need to perform another Sync to make sure the "change" has been implemented.
If not, then:
- Have you previously managed to Sync Podcasts with this iPod?
- Are they Podcasts, downloaded as Podcasts through iTunes?
- Are they iTunes U programmes?
- Are they video Podcasts?
- Do you see any error messages when you Sync the iPod with iTunes?
- Where, on your iPod, are you looking for the Podcasts?