My experience has been that, when they malfunction, the wall switches stop responding to controllers, and they stop dimming. You did not specify, but I'm guessing that yours is dead, i.e., no lights.
To diagnose, remove the switch and install it in a permanently-connected incandescent light circuit, or test-bench it with a plug, lamp, and wire. Also, don't assume your lamp is working, unless that's what you tested the plug-in module with.
It sounds like you have what's known as split-wired receptacles, half hot, half on a switch. Best bet is to rewire so the socket is always hot, and use a multi-button transmitter where the switch is.
I agree with EXT that, even if YOU know to not plug in something besides a lamp, somebody else (mother-in-law, maid, kids, etc.) may NOT know better.
Bye-bye switch.
Larry