Ben,
This error is occurring because the R process is attempting to pop-up a console window. And for MacOSX, only the root user can start the MacOSX windows services.

Since this worked previously and has just recently stopped, has anything changed on the server (i.e. has the OS been upgraded, installed a new version of R, etc)

For other unix type operating systems, we require the configuration of a X Windowing system (usually in the form of the X Virtual Frame buffer). Are you using X Virtual Frame Buffer for you server and maybe it is not started?

-Brian