Check to make sure that the episodes are downloaded. Look in the Podcasts section of your iTunes Library:
Looking at the screenshot above, note the cloud icon next to some (but not all) of the episodes for this specific Podcast. To copy episodes to your device, the episode needs to be downloaded (saved) on to your computer. In addition, if you have set your iTunes to Sync only unplayed episodes, then obviously any marked as fully played will not be copied onto your device. (Part-played episodes have a half blue circle to the left.)
Note that the Show: setting (pictured below) is not intuitive and displays only what it feels like showing. If I set it to Show: Saved Episodes, it fails to show episodes that are definitely on my computer (I checked while writing this post). You need to ensure that what iTunes is showing you is correct. I have no idea why Apple have made this such a poor user experience:
It never used to be like that and I don't understand why it is now (and has been for a long time). It makes no sense. To my mind, the "cloud" episodes should only be displayed as shown above if I select Show: Feed, not when I'm trying to work only with episodes that are in my Library.
