Loop Recorder can capture music from the web radio:
The loop mode infinitely records up to a specified number of minutes in a continuous loop while scrolling the data.
At any time the current data can be previewed and songs can be cut and saved as WAV or MP3-files, while the recording continues in the background. So you can always save the recently played songs.
I may try this out to capture Jim’s rants on WWR I miss while at work.