There are many reasons why this could occur. Some deal with how old your is and how it is constructed, old plaster or drywall. Or if there is a surface contaminate under the layers of paint.
A surface contaminate is the most likely cause. Try this to remedy the situation;
1) Wipe the chalky areas with a soft cloth and warm water. Allow to dry.
2) Apply two coats of tinted shellac primer to the spots. You can use a shellac primer in a spray can for more convenience. Allow 10-15 minutes between the coats.
3) Touch up the areas and see if the spots reoccur.
Another possibility is water getting into the wall and finding its way to the paint. Water inside a masonry type of surface will cause chalky areas. In this case find out where the water is coming from and repair. Treat the surface the same as above.
If the spots reoccur, you might have to try another type of primer. Try an oil base if this occurs. A shellac primer usually seals all stains. But, the contaminate could react with it.