This sounds like the same problem I have with flashlight batteries not making a good connection inside the flashlight. they work ok for a while, then become intermittent. If I shake the flashlight, bingo, but it soon fails again. The batteries are still ok b/c if I take them out, reposition, and put them back in again the flashlight works again. So the problem is at the connection between the batteries and the flashlight spring/clips. When I look at those I see no corrosion or dirt or anything unusual. I think what happens is the current flow when the flashlight is on is causing some kind of electrochemical plating of those metal part, and an oxide is forming which has a high resistance. If you’ve ever tried to solder to those kinds of connections, you know it doesn’t take solder well, so the metal must be some kind of alloy. Probably an aluminum alloy, and the resistive oxide that forms is aluminum oxide, which looks similar to aluminum metal and is why you can’t clearly see it.
Here’s my take: You won’t be able to fix this problem long-term. If you buy another one of those gadgets, the same thing will happen. If I had that problem I’d find the wires going to the cigarette lighter under the dash and splice into them with a connector pigtail, and put the other sex of that connector onto your usb charger wires. Cut off the adapter in other words, and replace with the matching connector. Then you’d always have a good connection available for charging your phone using the cig lighter’s fused circuit. Some caution is needed in choosing the style of connectors b/c the one connected under the dash will be hot at all times. You don’t want any exposed metal on that side of the connector.
I wish flashlight batteries came with little connectors rather than the point contact method they now use, so I wouldn’t have to battle this problem with my flashlights. I don’t think I’ve ever had a flashlight that didn’t develop this problem eventually. Any battery manufactures listening?