I had the same problem, did a ton of research on it, even called nokia/msft support (and was told they don't support 8.1 yet). Finally I ran across a one sentence explanation on some support page that said essentially that one must subscribe to a podcast series to be able to download individual podcasts. Otherwise one can only stream it.
I'm almost certain this I'd different than in 8.0, where you could download a podcast without subscribing to it.