<p>My initial tests have shown that Robot won't work without an active, visible desktop. For example, while a scheduled task (or executed command from the continuous integration server) may be able to start robot as a command-line process, Robot will actually fail to execute the recorded script.</p>

<p>Logging into the build machine to allow it an "active desktop" is not an acceptable solution.</p>

<p>Am I missing something? Is it possible to run a pre-recorded Rational Robot script on a continuous integration server in a manner that doesn't require the machine to be physically logged into?</p>

You can run Rational Robot from the command line, so you should be able to set up a scheduled task to run a .BAT file to do this for you. The command is something like:
[path to Rational Robot]\rtrobo [script file] /user "user name" /project [project file] /play /build "build name" /nolog /close
The Robot documentation will have other arguments you can pass in, depending on your situation.
If a simple scheduled task doesn't work, then you can try setting up a STAF (
http://staf.sourceforge.net/index.php
) environment and create a job to run this.
Good luck :)