I need a good podcast catcher (and a bit of a rant)

I listen to podcasts on my daily commute. These are radio shows that can be downloaded over the internet and listened to later. However, to keep up with a weekly show, I’d have to - every week - visit the show's website and manually download the latest episode. That would get real tedious real fast. To resolve the tedium for us all, the podcast catcher app was invented.

Podcast catchers allow me to list all the shows I want to listen to. Every day or so, it automatically checks each show on the list to see there are any new episodes for me. If it finds any, it downloads them and plays them for me.

Currently, I use Google’s ‘Listen’ app, but that service is about to be closed down with the imminent closure of Google Reader. I need to replace it. I've downloaded a handful of alternative apps, but they all lacked a feature I find essential. I remain a little flabbergasted that any podcast app out there does it any other way.