BUTTE, Montana (AP) — At least 786 children died of abuse or neglect in the U.S. in a six-year span in plain view of child protection authorities — many of them beaten, starved or left alone to drown while agencies had good reason to know they were in danger, The Associated Press has found.

To determine that number, the AP canvassed the 50 states, the District of Columbia and branches of the military — circumventing a system that does a terrible job of accounting for child deaths. Many states struggled to provide numbers. Secrecy often prevailed.

Most of the 786 children whose cases were compiled by the AP were under the age of 4. They lost their lives even as authorities were investigating their families or providing some form of protective services because of previous instances of neglect or violence or other troubles in the home.

Take Mattisyn Blaz, a 2-month-old Montana girl who died when her father spiked her "like a football," in the words of a prosecutor.

Matthew Blaz was well-known to child services personnel and police. Just two weeks after Mattisyn was born on June 25, 2013, he came home drunk, grabbed his wife by her hair and threw her to the kitchen floor while she clung to the newborn.

Jennifer Blaz said a child protective services worker visited the day after her husband's attack, spoke with her briefly and left. Her husband pleaded guilty to assault and was ordered by a judge to take anger management classes and stay away from his wife. Convinced he had changed, his wife allowed him to return to the home.

She said the next official contact between the family and Montana child services came more than six weeks later — the day of Mattisyn's funeral.

The system also failed Ethan Henderson, who was only 10 weeks old but already had been treated for a broken arm when his father hurled him into a recliner so hard that it caused a fatal brain injury.

Maine hotline workers had received at least 13 calls warning that Ethan or his siblings were suffering abuse. The caseworker who inspected the family's cramped trailer six days before Ethan died on May 8, 2012, wrote that the baby appeared "well cared for and safe in the care of his parents."

Many factors can contribute to the abuse dilemma nationwide: The child protective services system is plagued with worker shortages and a serious overload of cases. Budgets are tight, and nearly 40 percent of the 3 million child abuse and neglect complaints made annually to child protective services hotlines are "screened out" and never investigated.

Also, insufficient training for those who answer child abuse hotlines leads to reports being misclassified, sometimes with deadly consequences; a lack of a comprehensive national child welfare database allows some abusers to avoid detection by moving to different states; and a policy that promotes keeping families intact can play a major role in the number of deaths.

Because no single, complete set of data exists for the deaths of children who already were being overseen by child welfare caseworkers, the information compiled over the course of AP's eight-month investigation represents the most comprehensive statistics publicly available.

But the number of abuse and neglect fatalities where a prior open case existed at the time of death is undoubtedly much higher than the tally of 760.

Seven states reported a total of 230 open-case child deaths over the six-year period, but those were not included in the AP count because the states could not make a distinction between investigations started due to the incident that ultimately led to a child's death and cases that already were open when the child received the fatal injury.

The data collection system on child deaths is so flawed that no one can even say with accuracy how many children overall die from abuse or neglect every year. The federal government estimates an average of about 1,650 deaths annually in recent years; many believe the actual number is twice as high.

Even more lacking is comprehensive, publicly available data about the number of children dying while the subject of an open case or receiving assistance from the agencies that exist to keep them safe — the focus of AP's reporting.

"We all agree that we cannot solve a problem this complex until we agree it exists," said David Sanders, chairman of the federal Commission to Eliminate Child Abuse and Neglect Fatalities, whose members are traveling the country studying child deaths under a congressional mandate.

States submit information on child abuse deaths to the federal government on a voluntary basis — some of it comprehensive, some of it inaccurate. In some cases, states withhold information about child deaths in violation of the terms of federal grants they receive.

The U.S Department of Health and Human Services says all states receiving grants under a prevention and treatment program must "allow the public to access information when child abuse or neglect results in a child fatality," unless those details would put children, their families or those who report abuse at risk, or jeopardize an investigation.

Still, no state has ever been found in violation of disclosure requirements and federal grants have never been withheld, according to Catherine Nolan, who directs the Office on Child Abuse and Neglect, a sub-agency of HHS.

The information that states send the federal government through the voluntary system also is severely lacking.

A 2013 report showed that 17 states did not provide the federal government with a key measure of performance: how many children had died of child abuse after being removed from their homes and then reunited with their families within a five-year period.

When President Richard Nixon signed the Child Abuse Prevention and Treatment Act into law in 1974, it was seen as a sign of federal commitment to preventing child abuse through state-level monitoring.

But in 1995, a board reviewing the subsequent progress issued a scathing report calling or better information and transparency and flagging "serious gaps in data collection."

Nearly 20 years later — 40 years after Nixon signed the act — the AP found that many such problems persist.