Duh, I just tried it and it works.
I'm now feeling very stupid
That's really weird. I'm sure I used to get an error message when I tried to open more than one instance of Reaper.
edit. In fact I'm positive I used to have a problem. I wonder whether installing Vista service pack 1 has caused the change.
edit again: Something has definitely changed. I can now run Itunes, Media Player and Reaper all at the same time. That never used to work. Although I haven't tried it for a while, so I can't be certain the Vista SP1 update has caused the change.
Pete