Hello,
There are a few possibilities, the actual laptop charging DC socket being loose inside due to a break in the solder joints or its just worn out. This one will require a person with the right skills to check and if replacement is required it's an easy fix but soldering / desoldering will be required.
The actual power cable, is it ok as sometimes depending on how it was kept and used the wire can get knotted causing a break within the cable. This part of the plug which goes into the laptop can also degrade over time, get loose or due to heat melt internally. You would need a new power supply to test if this is the problem.
If you have it charging and all it takes is a small touch to disconnect the power then it is likely the laptop DC socket in which case take it to a repair shop or someone that can do the work.
