I guess I read the documentation wrong - "The (RR501) Transceiver Module receives radio frequency (RF) commands .... The Transceiver Module also passes on commands over your house wiring to control other X10 modules." I took that to mean the RR501 would pass along commands to other modules regardless of the source of the commands.
When I commented on using the CM11A, all the modules (RR501 and LM's) were set to the same code. The AH interface was not sending anything to a LM using that code. The only device the AH software knew about with that code was the RR501. Some of the time, using the CM11A, the LM's functioned, both on and off, even though AH did not know about them. At least as far as the AH screen on my PC looked. I routinely download timers and verify that the CM and the software are in sync.
I have a rotating Christmas tree and its light strings connected directly to the RR501. The LM's are plugged in around the house controlling various aspects of our Christmas decor. Some of the XPS3 switches, which turn CFL's on and off consistently on a schedule, are further away from the CM11A than some of the LM's which turn lights on and off intermittently. The remote controlled RR501 and LM's always work on the appropriate button push.
My guess is: The XPS3's don't need as strong a signal as the LM's and I have some sort of 'signal sucker' taking the signal strength below the LM-needed threshold but not low enough to impact the XSP3's.