Podcast playback stops shortly after beginning of podcast

I'm having a recurring problem with playback. When starting a new podcast, playback suddenly stops about 30-45 seconds into playing. I'm frequently listening to podcasts while underground in the New York subway. This may be a side effect of being within cellular reception and then leaving reception. That's only a guess, but if that's really the case then I would say that it's incredibly frustrating that playback of a fully downloaded podcast should require any network connectivity.

I'm experiencing this frequently -- most mornings on the way to work.