The butter or shortening theory may have merit, however fat content migrating through a water based field seems unlikely unless the cookie is still hot or liquid oil was used. Again there are so many variables and each one would need to be eliminated. With a dry surface a lightly sprayed simple syrup coating will "encapsulate the cookie surface with a protective barrier.
If you are using a quality color like the AmeriColor Soft Gel Paste, then it is probably not the color causing the problem, however less advanced secondary and tertiary color systems may separate into primary their stages.