Check your fuses. The main body feed supplies power. There is also a fuse under the lighter.
My back door lighters had not worked for many years since owning my car. I did have 12 V to them but the power wasn't getting thru. I opened that small round block under the holder and found remnants of a disc and white powder. I think this was a bi-metallic disc to prevent overheating. Kids might want to keep it from popping up. (?) Anyway after it would cool ,it would work again, instead of blowing that important body feed fuse. I used holders from front lighters ,( parts car),and they work great now. HTH