Since it's the same podcasts, I'm going with it's the podcasts' fault, not the apps. Podcast producers are responsible for storage/server to host their podcasts and the apps are going to those servers to get the episodes, including Apple's podcasts app.
For example, here's the path to Conan O'Brien's podcast episode with John Cleese in Apple's Podcasts app database:
Code:
https://chtbl.com/track/9E9755/stitcher.simplecastaudio.com/c945bd13-c7f3-4f22-95b5-4bf98e12b21f/episodes/29f0016f-05e0-4610-9fc5-824183808bf6/audio/128/default.mp3?aid=rss_feed&awCollectionId=c945bd13-c7f3-4f22-95b5-4bf98e12b21f&awEpisodeId=29f0016f-05e0-4610-9fc5-824183808bf6&feed=dHoohVNH
So, server errors, not publishing properly, no longer publishing, other? Anything but the app(s) or OS fault.