Paint won't stick to my plaster walls?

I bought a house that was built in 1955. My room is a ';lovely'; 1950's bright yellow. I have tried several different brands of paint and none of them stick to the walls. It peels off like paper. It great big pieces. None of the other rooms in the house have this problem. I painted white, it peeled, then I painted a brown color, where the new paint is peeling, both colors are coming off together. It's awful looking. I can actually sit in there and peel an entire wall with just my fingers! (not that I've tried, but I'm at that point). Any suggestions on what to do????? Please, help me!Paint won't stick to my plaster walls?
Skim coat the wall, or add a layer of drywall over the plaster.