Unless you mean that you have a *PORTABLE* 12v car battery that's not part of a car, and you just happen to be using a cig lighter style socket as the connector. Then my suggestion is moot.

Hm. Unless the connector plug to the socket has an iffy ground. I personally have had nothing but trouble with Cig-style sockets in the past. Sometimes you get good solid ones and sometimes the connections are poor. Do your problems go away if you throw away the Cig-style sockets and connect the wires directly the battery terminals?