I manage a podcast feed for my church, and recently had a problem where I was unable to download episodes using the iOS Podcast app on my iPhone. The podcast would download OK on other Android devices, and it would stream on my iPhone if I tapped the play icon, but if I selected “Download Episode” then the download would appear to happen, but then at the end a message would pop up saying “Unable to download podcast”, with a “Retry” and a “Done” button.
Googling this problem shows that other people have experienced similar issues, but no amount of unsubscribing, deleting, restarting, rebooting, or switching to airplane mode would fix the problem.
In the end I discovered that the problem was due to a misconfiguration in the XML file for the podcast feed. In the <channel> section of the XML file there is an <itunes:image> tag where you can put the URL of an image. I discovered that this tag was pointing to an invalid URL, to a server that I had used several years ago. After setting the tag to a valid URL, and refreshing the feed in the iOS podcast app, I was able to download episodes.