Did you tell it to download over cellular? If so, you can't download anything larger than ~30MB, and those will wait for wifi. Moreover, I found that my 920 didn't want to download podcasts over wifi unless I was also plugged in, which is not really convenient since my phone is only turned off when it's plugged in and wifi currently doesn't stay on when locked.
But the straw that broke the camel's back was that the Music app kept trying to download a non-existent episode of one of my podcasts, and even when I'd manually cancel the download it'd show back up as "pending" after an hour. I switched over to
wpodder and just stream everything now. There are enough other halfway decent podcast apps that function better than the built-in, I don't see myself going back unless Microsoft puts a large amount of work into un-breaking podcasts.