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Hold the jack steady in the port and wiggle the cord near the base of the jack. If you still get intermittent connectivity, it's likely the cord. Another cord is called for, or a repair of the current cord if the open is far enough away from the jack, although that isn't really a great idea unless you simply can't afford a new cord.

If you get no change in connectivity, it's likely the port in the laptop. Some power ports on laptops will simply be a female receptacle that has a few wires running from it to a PCA inside the laptop, but typically, the solder joints on the port connect to the motherboard (or another PCA that the port is attached to) and have become cracked or separated from the PCA itself. This is a problematic issue that can sometimes be repaired by touching up the joints with a soldering iron and maybe a little more solder, but that also depends upon the design of the board itself. Tearing down the laptop to get to that port is no small task and you can easily damage your laptop further just from disassembly. More often than not, the board the port is on needs replaced.

Not a fun problem to resolve.