Tory councillors are calling for an investigation into the tragic case of four-year-old John Smith.
A catalogue of errors by social services was revealed in an inquiry report prepared for the Brighton and Hove and West Sussex area child protection committees.
Simon and Michelle McWilliam, who wanted to adopt John, were each jailed for eight years for child cruelty after the boy died while in their care.
The independent report by Alyson Leslie recommended many changes in practice by health and social workers, many of which have already been adopted.
Conservative group leader Brian Oxley said he and his colleagues were calling for a scrutiny investigation.
He said: "We want to look at the allegations the service is under extreme pressure."
He said an investigation should be held into whether that was partly responsible for the errors.
He added: "I was shocked by this case. You can understand one mistake but not a whole catalogue of them."
Former Tory leader Geoffrey Theobald is calling for the resignation of social care Cabinet member Jean Spray.
He said this case followed the Palmeira Project affair, when parents of autistic children successfully fought the decision of NCH and the council to close their home.
In another child cruelty case two years ago, three youngsters died after living in appalling conditions.
Coun Theobald said: "The executive councillor should consider her position after all these problems. The administration is facing one problem after another."
Coun Jean Spray said: "Many of the recommendations have been acted upon and Alyson Leslie has praised the council's response to it."
She said the request for scrutiny would have to be considered, adding: "We would have to be sure it was not duplicating work that had already been done."
She said there were tremendous pressures on the social care department and on social workers.
There were problems in recruiting and retaining these officers, who had to act as the eyes and ears of the public.
Coun Spray brushed off the call for her resignation.
There had been pressure on both her and social care director Allan Bowman but they intended to continue their work, which included further reaction to the case and the report.
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