As don't know the specifics of your install, I can only make a couple of assumptions and suggestions
I assume this install was done in the 2013 JK listed in your profile
Your JK has the new and improved CANBus system. Read as: never ever ever tap into power or ground on your existing wiring harness
First, if you are pulling power direct from the battery, an sPod, or something similar than all things point to ground fault. If you are pulling power from the harness see above. Cigarette lighter plugs are not friendly either for CB use.
Best practice for any transceiver install is to make sure the entire system is grounded very well. A braided copper ground strap at the antenna mount connected to a clean and unpainted frame ground is preferred. Power ground to negative battery terminal also your best bet.
Another thing is that you mentioned using a 102 whip. These are outstanding antennas until you tie them down. One must remember that a CB radio aka 11 meter, is an HF radio. HF radios (anything that runs 3 to 30Mhz) can play hell on automotive electronic/electrical systems.
The radio wave emanating or propagating from the antenna looks like this when its vertical
When bent over and tied down that donut of radio waves is now pointing into your jeep and up in the sky, but I digress
Good grounding and proper power source should solve the problem.
Quite frankly I wish I could run a 102 whip on mine but they aren't allowed most places due to the hazard they pose to people outside the vehicle e.g. spotters getting hit with them. They are an extremely efficient antenna.
