iTunes app on iPhone won't download podcasts
I feel like I helped my brother through something VERY similar involving downloaded/purchased music -- and the only thing we found that fixed it was a complete restore from his most recent backup. I surmised that it was something related to a horked cache file or setting at the OS level.

The other thing that it might have been related to was wifi syncing/backup; we also turned that off, if I recall, and it wasn't until it was turned off that things returned to copacetic.

This is all fuzzy memory from months ago, though, so YMMV.