First off, never wiggle a USB plug. The parts that make the connection are quite a bit more delicate than a wall plug and wiggling it will damage them. Instead, grip the plug itself, not the wire, and pull or push straight out/in.
Second, USB plugs are notorious for getting gunk in them. Try using canned air to blast a couple of quick jets into both halves of the connection. You can also disconnect the cable and turn the power off on the unit, then twirl the end of a paper towel into a point and dip it into 91% rubbing alcohol, press out the excess and carefully clean out the connect points. Let it dry thoroughly before reusing.
If cleaning the USB doesn't work, the typical failure point to any USB rechargeable is the cable, thanks to the delicate copper wire inside and the fact that many are of cheap Chinese make. Try purchasing and/or using a quality replacement.