The power cord will not stay plugged into my computer. Unfortunately this is the 3rd time it has happened. The previous two times it was under warranty. The cord was replaced and that worked for a while. Now it has happened again and I am beginning to think it is not the cord, but where it plugs into the computer that is faulty. Any advice?

If it is that loose it is worn out in the case on the mother board now this is a simple replacement of a little plastic adapter. They are relatively inexpensive but the repair is not. It is complete removal of parts from the lap top to get to this part. If not done correctly your lap top will suffer serious issues and may have to have the whole board replaced. I strongly advise that you take this in to a repair shop or make it work by gently take a pair of pliers "Needle Nose" and gently squeeze the tip I mean gently so as to not break the wiring seal or anything else. Do it just enough to stay on the pin on your lap top.
Take this in if you can afford it and get it done properly is my first option. You are responsible for it if you go with that suggestion of a gentle squeeze not much very gentle and once until it stays in that is all. This is what I would do first it is cheaper to replace another cord than a board repair. John