Hello, let me tell you straightly, let us pool our ideas, we should find an ideal solution. How about this sound recorder that claims to record live internet audio or radio coming from computer's sound card. Hope you join us to discuss.
I use a command line program called mplayer. It's a media player, and can stream on HTTP, FTP, MMS or RTSP/RTP. Here is an example on how to stream, and at the bottom it shows how to save a stream to a file.
Note, you will need the actual URL of the stream. To do this, you will probably need to look at the source code of the page that has the online radio player. It should be around there somewhere, if you have trouble finding it, try searching for "http" in the source, or whichever protocol it uses, because it's likely to have the full path [Instead of, for example, /stream.asf]