I'm also experiencing this problem. I've tried deleting the app, resetting the phone... un/re sunscribing. Nothing works.
What I did before all this broke:
1 - I have iTunes on my macbook download the podcasts
2 - Set to auto transfer all unwatched episodes of about a dozen podcasts
3 - Sync my phone in the morning, loaded up with all new podcasts
4 - Listen to podcasts in my car (without eating the battery or my data by transferring from the cloud)
What I do now:
1 - Check iTunes and see that it missed episodes of some podcasts
2 - Manually download the episodes that didn't automatically download
3 - Verify that, yes, all the podcasts are set to auto download latest unwatched episodes
4 - Bang head into desk
5 - Hit sync, watch the progress bar sometimes transfer a podcast, most of the time not
6 - Check the podcast app on the phone and see that no podcasts have transferred (despite there being 20+ unwatched episodes)
7 - Verify all the settings in iTunes/phone
8 - Sit there contimplating throwing the phone down the garbage disposal
9 - Curse apple for breaking something that worked perfectly before...
10 - Repeat steps 1-9, etc
What I'm seeing on the phone is exactly what the previous posters described. My podcasts do not transfer, and the icloud download icon shows available. I can steam from the cloud, not that I want to eat my cell data, but that is the only way to hear my podcasts.
What I don't understand, is that it works the same way, regardless of the settings on my phone. I've tried both sync podcasts and don't sync, manually sync, auto sync, etc... all the combos of settings on the phone and iTunes. I can't get any of them to work.
The fact that iTunes on the MacOS is also broken makes me think there is something more systemic than just the podcast app or iOS being broken. Either that or it's tinfoil hat time, and it is a conspiracy between apple and the carriers to get us to use more data so they can charge more...
Really hoping it isn't tinfoil hat time. I hate tinfoil hat time.