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From my own experience the cig lighter ports in these cars can be a little finicky. I had the same issue where 12V was there and the lighter would heat up, but no USB power. Turns out I just needed to push it in a little further. Still isn't completely reliable but I'm fairly certain it's just a contact issue like KC mentioned.
It does sound as though the connection is poor. Does the USB charger fit snugly into the cigarette lighter? Sometimes if they are not fully seated they can slump over to one side and lose connection.
Cleaned it out with a wire push and cloth, and sprayed electrical contact cleaner, let it dry out, popped in and retried the OEM lighter plunger - it worked fine.
Pushed in USB half the way, 3/4 of the way, all the way, twisted it, turned it...nothing. And I know it works, just took it out my truck.
I had an issue with the cigarette lighter having a poor and intermittent connection. My problem was that the 12V bullet connector that plugs to the back of the cigarette lighter was loose and corroded. Solution was to take the dash apart and either clean and crush the connector a little to make a tighter connection, or cut it off and replace it with an appropriately sized female bullet connector (make sure it's a covered connector or use heat shrink, it's a high risk of shorting when you reinstall the dash if you don't). Might as well clean up the ground connection if you have it open, too.
I have a similar issue. sometimes you just have to spin it around a bit until it makes contact.. it's in my backlog of features/issues to work through.
I know that our cars always have had wiring problems dueue to age... so I know that I will have the same problem so I'll be wiring one of these in...not sure if it's going to be this one exactly but definitely will be wiring one in....