Powys County Council says it is not yet ready to appoint a new director of education despite restoring and re-advertising the role.
It was scrapped in a management shake-up last year, with Alec Clark running the service as head of education until he left for another job in August.
Chief executive Dr Caroline Turner said the council was looking for a "truly exceptional" candidate to take charge.
Estyn inspectors have criticised many Powys secondary schools as "weak".
They said in a report in September they also had "significant concern" about school finances, surplus places and a high exclusion rate.
In July, Powys council leaders backed a report by Dr Turner recommending they bring back the position of director of education.
An advertisement for the job - on a salary of £85,000 to £92,547 - was published in October, saying: "Whilst Powys has a number of strengths in educational standards, we have our improvement challenges."
But following the close of applications on Sunday, Dr Turner said: "We were not successful at our first attempt to fill this crucial role."
She said: "We are looking for a truly exceptional candidate who will lead us on our improvement journey to provide outstanding education services for future generations.
"Education in Powys is facing huge challenges and needs to radically change."