I live in a house built in 1959. Not sure if ceiling is sheetrock or plaster. Although I don't have any 'stains' or obvious leaking, even during heavy rains, in a couple of different rooms I have a flaky, almost cottage cheese texture in a small area. In one bathroom, I have flaking ceiling paint, even though the bathtub in that room is rarely used. I have repainted that one at least twice, even with a primer and Kilz, but it flakes again after a while. In the other spots, the 'cheesy' paint can be sanded off. Does this sound like a leaky ceiling or bad paint?
The powdery, 'cheesy' places are definitely a roof or ac vent leak.
The flaking paint, if not accompanied by the cheesiness, is probably just a latex-over-oil issue. Even with multiple layers of cure-all primers and stain killers, some bad paints can't be cured. Try a primer called 'bonding primer'. It should work well to gather up the particulates and really, as the name implies, bond the paintjob together. Go two good coats of this newer style 'paint amd primer in one" paint junk that's so popular now. It's not really primer, just a thickened paint, but it may help to isolate your issue.
If that fails, might be time to start thinking of furring the ceiling down and installing a new one.