To give one of the most accurate descriptions on reporting the incidents of child abuse, I refer you to the Fourth Annual Incidence Study of Child Abuse and Neglect (NIS-4) conducted by Westat, Inc. for the U.S. Department of Health and Human Services which provides the following information.
Although CPS (Child Protective Services) investigates a substantial number of the maltreated children in the nation, these children represent only the tip of the iceberg.
Other children, a second level are investigated by law enforcement agencies, courts, or public health departments. Although they are recognized as maltreated, “these children are not investigated by CPS because questions of definition or disputes concerning the appropriate responsibilities of these different agencies arise in relation to CPS.” They do not necessarily receive assistance that specifically targets their abuse or neglect problems.
The third level includes abused and neglected children who are not investigated by CPS and who are not recognized as maltreated at any agency in the second level listed above but who are known to professionals in other major community institutions, such as schools, hospitals, mental health agencies, day care centers, shelters, public housing agencies, and other social services agencies. Children may remain at this level because the professional who recognized their maltreatment did report them, but CPS declined to accept their cases for investigation because the professional did not provide sufficient information to CPS to warrant investigation.
The fourth level, someone outside the purview of the first three levels recognizes the abused the abused and neglected children as maltreated, such as a neighbor, another member of the family, or one or both of the involved parties—the perpetrator and the child victim. However, no one at this level has disclosed the maltreatment to anyone in the first three levels.
In the fifth level are those children no one recognizes as maltreated. These are cases where the individuals involved do not themselves regard their behavior or experiences as child maltreatment and where their situations have not come to the attention of outside observers who would identify them as abused and/or neglected.
This description of why most child abuse is not reported is the most accurate I could find.
 Sedlak, A.J., Mettenburg, J., Basena, M., Petta, I., McPherson, J., Greene, A., and Li, S. (2010). Fourth National Incidence Study of Child Abuse (NIS-4): Report to Congress, Washington, DC: U.S. Department of Health and Human Services, Administration for Children and Families http://www.acf.hhs.gov/sites/default/files/opre/nis4_report_congress_full_pdf_jan2010.pdf