Now one problem is that my internet connection isn't always the greatest. Plus some of these archives are time limited (only showing the last six months or a year). And unfortunately you can't directly save the streams from the browser (even if you open up the ASF and try to decode the contents). The MMA protocol gets redirected to the windows media player in any case. So off we go on another Google search.
ten seconds pass
Besides a number of programs people are trying to sell to do this, it turns out a group calling themselves the Streaming Download Project decided to write software to do it for free. Unfortunately it only runs in real time (taking an hour to download a 4MB audio file), but you can batch up multiple requests and just let it run in the background. I'm running a capture right now, looks like it works.