Standard players for RTSP streams like those for RealAudio don’t cache the files they download, meaning they require a net connection to operate. I found an EZBoard forum message that identified HiDownload, Net Transport, OEP-OEE and StreamDown — Windows-only applications that can download RTSP streams and save them to a playable file. But those trick ponies do nothing to help Mac users.
AudioHijack has been around for years now, but it only captures the audio stream as it leaves RealPlayer and heads off to your Mac’s audio output. This works, but it has its own problems. Googling turned up a discussion of what I was looking for, this list QuickTime utilities, and this discussion of how AirTunes and AirPort Express interact. But I found no real answers. Darn.