Podcast app failed to sync on iOS, and how to resolve it

I recently updated my iPad 3 with iOS 6 to iOS 7.x.x .  Everything seemed to be working fine.  But then last night I found out that the Podcast app didn't sync my podcast subscription with my iPod Touch gen 5 and iPad 2, both running iOS 7.

Solution?  Delete the Podcast app on my iPad 3, and then reinstall again.  Problem solved.