I'd try the typical things (look for new electronics, try an alternate device in the socket, try a different socket, try a different location for the controller, etc). Typically when something stops working right, it's related to a new device (phone charger) or a device going bad (CFL, the device being controlled) or the module (supersocket in this case). The peculiar thing is that normally you can turn the device on but it won't respond to off.
You said that you can control the module via a Palm Pad. Is AHP connected to the same controller you are using to transceive the remote's signals? If you are using a CM15A then that is possible. I don't know when the CM15A was released, but I see references to it from 2006, so it's possible that you have one since you mentioned this has worked for 10+ years. If not, then you must be using one controller with AHP and another to transceive wireless. If that's the case, then you would be injecting the X10 signal from different locations at different signal strengths.