With iOS6 has come a change in how Podcasts are handled. The standalone Podcasts app now handles e on-device updating, but then overrides the Music app stopping it from being able to see the Podcasts category. This also then removes any podcasts from your playlists,
You can switch back to using Music to handle the playback, but this does come at the expense of losing the on-device updating. You can then only update podcasts on Desktop iTunes.
This is less than idea, but until Apple fix playlisting in the Podcasts app itself (or allow podcasts to coexist in both apps like they could in iOS5), you have to choose between playlisting and on-device downloading.
- Delete the Podcasts app
- Stop the Music app
- Shut down and restart your iOS device
Podcasts are now once more in their own category in Music, and your playlists will have returned.
Hopefully Apple will returning playlisting functionalty to the Podcasts app so that podcasts can be both updated and playlisted from the device itself.
Information found from the Apple Discussions forum, and other sources. Verified as working on my iPad. Put in a place I can remember, so I can put the link out whenever I see people hitting this particular design oversight.