I recommend using a sigle shared (Singleton) UIManagedDocument to ensure that you have the same UIManagedObjectContext for all the classes in your App.
Example on how to set this up can be found in thos blog:
http://www.adevelopingstory.com/blog/2012/03/core-data-with-a-single-shared-uimanageddocument.html
You can have several NSFetchedResultsController that will use this shared UIManagedObjectContext (from the shared UIManagedDocument).
This is a sample project I did for the Stanford course CS193p on iPhone programming. It uses Core Data with the sigleton I am proposing.