The corporate director for children, schools and families services at Cornwall Council has resigned.
Dean Ashton said children's social care within the county had not improved enough in recent years.
An unannounced Ofsted inspection in July said children's services access and assessment teams referrals "were not always promptly responded to".
The council said that interim arrangements were being put in place to cover Mr Ashton's post.
The council said that it knew that an Ofsted inspection of referral services in the department in July had confirmed the quality of practise was inconsistent.
A letter from Ofsted about the unannounced inspection seen by the BBC said referrals were not always promptly responded to, including for "some children concerned with child protection".
It said: "For example, delay in receiving police notifications of domestic violence incidents is reducing the council's ability to safeguard children and young people."
It added that a number of children had to have three or more repeat referrals before being accepted as cases for intervention.
Another Ofsted inspection was carried out in September. The report on that is due out later this month.
Cornwall Council said the interim arrangements for leading the directorate were being finalised and would be "announced shortly".
Children's services in the county were criticised in another report earlier this year.
The unitary authority Cornwall Council took over social services from the former county council when it was formed in April.
However, in March the Audit Commission told the county council it was not making adequate improvements.
The commission said some aspects of children's services had not improved, and the council was poor at setting its priorities and performance management had remained weak.