I have "Delete Played Episodes" turned OFF for all my podcasts, both on the iPhone AND in my PC iTunes.
Whenever I finish playing an episode on the phone, the episode name remains visible but the audio content is deleted and a "cloud" icon appears next to the name.
What magic incantation do I need to utter to make the podcast player leave the podcasts on the device? Clearly "Delete Played Episodes-OFF" must be in some alien language that happens to have certain words matching English but means something completely different.