Thats probably my issue, I usually close my apps, but I was leaving this one open in the background like I do with ubertwitter so that my podcasts are already downloaded automatically when I want to listen to them.
I will try only opening it to download the podcasts and closing it after.
Mine will download podcasts even if it's not running in the background. It notifies me, then just starts downloading. One came through last night when I was mowing the lawn. I checked my phone, had the new podcast notification and when I opened the app, it had already downloaded.
One thing I have noticed about this app...you sometimes can shut it down, but the medial player will still be up and running. But it won't show up in your open apps menu. I finally figured this out when I kept hitting the menu button and saw a "podcasts currently playing" choice. Selecting that opened the media player and I was able to shut it down.