Because the WS12A does not use a neutral connection, the leakage current supplies power to its control circuitry as well as being the return path for X10 signals. Lamp modules have a neutral connection, so they do not need to pass any current through the load.
The easy fix is to include one incandescent light in the string to provide a low resistance path for the leakage current. The other option is to choose a dimmer switch that includes a neutral connection. The Leviton switches we installed here included neutral connections, but they have been discontinued by Leviton. If you only need one, I do have a couple of "pre-owned" Leviton dimmers that you could have for half of wholesale. Contact me by email if interested.
I believe some Insteon dimmers still support the X10 protocol, and they include the neutral connection. So that may be another option.