OK, I found out what happens with the RSS button in IE7. If I come to this site and I am not signed in, the RSS button appears.
If I am signed in, I am shown a different version of the home page, one with lots of features ready for me to click and adjust. That one apparently doesn’t have an RSS feed set up for discovery.
Mystery solved. A little disconcerting, but I can deal with it. It also serves as a reminder that I should be signed out if I want to see this Live Spaces the way visitors do.