The tip that abuse was taking place in the Long Beach home where 2-year-old Joseph Byrd lived came to Los Angeles County child welfare officials nearly two months ago.

But 57 days after opening an investigation into the allegations, social workers had yet to determine if Joseph was at risk when the toddler was pronounced dead Saturday. Coroner's officials have listed the case as a homicide.

At the time of Joseph's death, social workers were still looking into allegations of abuse and neglect in a family that already had been investigated five times, according to sources familiar with their history. Three of those cases were substantiated, sources told The Times.

Joseph's case is a grim illustration of the growing number of abuse and neglect investigations still open past the state's 30-day deadline.

Despite pledges to resolve Los Angeles County's mounting backlog, the crisis has deepened significantly in recent weeks. At last count, cases involving more than 20,000 children reported at risk of abuse or neglect had not been fully investigated within 30 days - up from 18,000 in May. Even with a temporary extension allowing L.A. County 60 days to complete its inquiries, social workers were unable to meet the new deadline in 5,400 cases involving more than 12,000 children - up from 3,700 such cases last month.

Joseph's father told doctors at Long Beach Memorial Hospital that his son drowned in a bathtub while he was unattended. Authorities, however, have questioned his story. Coroner's records indicate suspicion that Joseph had ingested drugs, although tests to determine toxicology will not be complete for weeks.

Long Beach police officials this week asked for the public's help in determining what happened.

What is clear is that Department of Children and Family Service leaders continue to struggle to complete timely investigations.

"Right now, our caseloads for these workers are within the yardstick where we want to be," Supervisor Gloria Molina said Tuesday. "If you tell me we need more people to make the same dumb mistakes without proper supervision, I disagree."

In May, department head Trish Ploehn said additional staff was needed to expedite investigations.

"The social worker staff simply cannot keep up with everything we are asking them to do," she said, adding that she planned to make the case to county supervisors that hundreds of additional social workers were needed. "All of the things that equate with quality do take time."

In the end, Ploehn never submitted a budget request for additional social workers, citing the county's tight finances.

Instead, department officials have relied on temporary reassignments of existing staff members to the investigative unit, increasing the number of child abuse investigators to 992 from 596. Even so, the backlog has gotten worse, and many of those workers, whose regular jobs are considered essential, soon must return to their previous posts.

Supervisor Zev Yaroslavsky said there was "no excuse having a backlog of this magnitude" in a department that has grown to nearly 4,000 workers from about 2,900 nine years ago. He expressed growing frustration with what he described as a lack of strong management and reactive policymaking.

"Not only is their well-being on the line," he said of the children, "their lives are on the line."

Molina said there was "obviously" a deep disagreement over the department's direction.

"Right now, I am surprised she is not being more efficient and effective," she said of Ploehn. But Molina said Ploehn's job was not in jeopardy.

Lizelda Lopez, spokeswoman for the California Department of Social Services, said Tuesday that her agency remains supportive of L.A. County's efforts. The county, Lopez said, "is doing more than is required by regulations" in its child abuse investigations.

Ploehn also declined to respond to questions about the increasing number of cases that remain open past both deadlines. In a statement, she said the department was "legally unable to share any information on the details of this investigation until it is completed."

"The death of any child is tragic and heartbreaking, and it pains all of us whenever it happens, no matter the circumstances," Ploehn said. The increase in the backlog of cases was "consistent with seasonal trends," she said.

In recent months, Ploehn has dramatically reduced the number of child death case records released to the public. Under a law that went into effect in 2008, authorities are supposed to make public the records for child fatalities resulting from abuse or neglect. Department officials in L.A. County disclosed case histories in almost all such deaths that occurred in the first 18 months of the law.

After a series of stories on the deaths in The Times last year, the release of records slowed dramatically. Of the 23 most recent deaths resulting from abuse or neglect since June last year, the department has released limited records in only two cases, citing a provision in state regulations that allows the district attorney or police agencies to redact information that might jeopardize a criminal investigation. Without such disclosures, determining how many child fatalities in the county involve families or children with previous department involvement is essentially impossible.

Los Angeles County district attorney's officials told The Times that they have been unable to locate any staffers who objected to the release of the information in the cases where they have been cited as objectors. Department officials declined to identify the police agencies they say objected in the other cases.