This is so irritating!!! But this problem is tied to the syncing of podcasts across devices via iCloud. First off, Apple has no way of letting you "reset" your Podcast sync data. You can delete podcasts all you want, but if you subscribe again, it will still "remember" what has been played. Which is fine IF IT WORKED FLAWLESSLY!!
I've looked everywhere for a way to reset everything back to "blank slate"/"clean"... I can't find a way anywhere. I'm a developer and have tried all sorts of super behind the scene ways too.
What does this have to do with the question here? Well... I too have this problem with iTunes no longer refreshing podcasts (even when trying to do so manually). But guess what? Forget logging out of iCloud/iTunes/Apple ID... simply go to iTunes preferences and then under Store... uncheck the "sync podcasts subscriptions and settings"... now hit refresh and it works... then go back and toggle the setting again, it no longer works.
So again, this is related to Apple's problematic iCloud solution for podcasts. It just doesn't work well most of the time (and now for iTunes for me, not at all).
I'd love to know if anyone has a solution to reset Podcasts COMPLETELY (I'm sick of the weird little bugs that have accumulated over the last few years with this messy solution!). But meanwhile, my work around for this issue is to just manually refresh while toggling on and off this setting (and so far, it keeps things in sync, mostly, across mac and iDevices).