iTunes 12: How Do I Fix a Problem with a Podcast That iTunes Quit Downloading Episodes For?
Based on our troubleshooting in the Comments, the problem appears to be from the podcast provider's side.

Using two different podcast players in iOS, the last available episode for download was several weeks ago.  The latest version is not yet available.

By going directly to the podcast owner's site, the episode is playable directly from there.  It will not download to the podcast player, however. The OP will contact the podcast creator for further assistance.