You can pull the connector out and examine its condition, usually a little prong must be depressed on the wire side. The connector could be loose and corroded on the inside. High resistance makes these overheat, then the metals loose spring tension.
Cleaning the outside wont do much.
Usually these are tin coated, I have cleaned some of these with white vinegar, which can strip the tin. Then you can grease it or spray it with some oil.