Try this test. Make a strong solution of warm water and TSP, About 1 cup of TSP to a gallon of water. Chip away the pealing paint to expose an area of the old, chalky paint. Wet the exposed old paint with the TSP and keep it wet for about 5 minutes, then scrub the wet area with a scrub brush for a few minutes and then rinse it off with clear water. If all the paint comes off, then I'd have to say that cheap paint is the source of the problem.
"Hy" the peel-away-guy may stop in a give a better solution to the problem than I could. In any case, you need to get rid of the chalky paint. Fortunatly for you, we're talking about plaster and not drywall.
I have used this process for removing flaking paint from plaster. I go to a wallpaper store and get a heavy vinyl wallcovering, something with a woven fabric backing. It doesn't even matter if I get rolls of the same pattern, I just try to get something that the retailer is trying to get rid of to have it out of his/her way (this can take some searching, as only a woven fabric backed vinyl will work). I then paste this with heavy duty clay based adhesive and hang over the pealing paint (scraping the seriously loose stuff away first). I allow this to dry for several days, then when I rip the vinyl down, it takes the loose paint with it. Then I wash any adhesive off and now we have exposed the old chalky paint.
This is where I'm going to have to defer to someone else to come up with a better idea. I'd be tempted to wash and scrub the whole ceiling with TSP and rinse well, then prime it with an alkyd primer loaded to the maximum with "Penetrol" and a little "White" kerosene to extend it's drying time and allow it to fully penetrate the offending surface. However, I'm not certain that that will solve the problem once and for all.