Have you ever heard of Streamripper: http://streamripper.sourceforge.net/srdownloads.php
This is one killer program. I use a command line version with Linux, 1.32 I think. The tarball comes with good reference and is simple to use. I use it with Xmms. Use the "View File Info" selection in the menu to find the http: address of the stream, and start streamripper in a terminal. It rips streams at 128K and creates a folder for each stream address and names each individual mp3 within that folder. Kinda sounded what you might be looking for. Just thought I would throw it out here. Just don't share or distribute what you rip. You know. See Ya!
RE: Noticed you said no file to save or open so you may SOL with this unless you can find the http: stream address somehow. Sorry!