Keepvid only works with file formats where the entire file is downloaded, as a single item, to your PC.
The BBC uses 'streaming video'. That means that their server doesn't send you a single file. It sends you a stream of data, which is displayed on your screen, in the same way that your TV receives a stream of data through its aerial. If you want to record a TV program you need something (such as a VCR or a DVD-recorder) to record the stream and convert it to a single file, onto tape or a DVD. Similarly, you need a way to record streaming video, to capture it as a single file.
I'm not aware of any free software that will record streaming video from the Real Media format but this commercial program claims to do what you want. It also offers a free trial period, with full functionality, so (hopefully) it should meet your needs and enable you to record your son's moment of stardom:
http://www.streamingstar.com/hidownload.htm
Chris