Dan:
It sounds like the "local control" feature in the module is sensing a change in current and turning back on in response to it. The local control feature allows you to quickly switch the plugged in device on/off/on and the module will turn on without an X-10 ON signal. Since you have tried 3 different modules it is not likely that they are all defective.
Try connecting the module to a lamp (over 40 watts) and see if it works properly at the same location you have it now. If it does, then it is most likely the local control feature that is kicking in. There are some things you can do to solve a "local control" problem, including disabling the feature on the module. If you would like more information on how to do this, let me know what type of module you are using, and what the device's wattage,amps, and voltage.
Also, as Roland mentioned, do not exceed the wattage or amp ratings on any modules as it is not safe.
Robert
RCI Automation
rciautomation@compuserve.com[Link: ourworld.compuserve.com]