My power adaptor, occasionally, stops charging the laptop.

Commonly one would think they have a bad cord. But since you indicated you have to wiggle in the connection that would suggest that you either have some dirt or something in the connection, the end of the power cord itself was bad but I would moreso believe the connection inside the laptop was loose or broke a solder connection. Check the cord with a voltmeter while wiggling it to see if your voltage goes off and on to confirm. Inspect connection they do often collect dust. You’ll have to open up the laptop to see if you have a broken solder point or if the connection is loose.