A motion calling on Wakefield Council leader Peter Box to resign has been voted down.
The local authority's Conservative group had called on the long-serving Labour figurehead to stand down "immediately", following attempts by some of his own colleagues to replace him during weeks of unrest.
Councillor Box has been heavily criticised in some quarters of his own party for Wakefield's failing children's services, which could be taken out of the council's hands when a government commissioner reports in November.
Tory leader Nadeem Ahmed, who had previously backed Coun Box to deliver improvements to the service, said he had reversed his position because Labour's internal divisions were "distracting" them from council business.
Addressing the leader directly at a full council meeting, Coun Ahmed said: "It's come to a time where you have to ask whether some of the issues are down to your leadership.
"Of all leaders in West Yorkshire, you are the one that is falling behind, in terms of our (Wakefield's) influence across West Yorkshire. Your influence is very limited now.
"We're standing on a knife edge. I think that children's services is at risk. I don't see it being run by the council in the medium term.
"It's time for you to take responsibility, step aside and let fresh people take over from you."
But the Tories' motion was defeated by an amended version tabled by Labour, which watered down personal criticism of Coun Box but stated that he had to deliver improvements to children's services to "maintain confidence" in him.
George Ayre, one of only two Labour councillors to have publicly called for the leader to resign, questioned the Tories' motives for the motion, but was scathing of senior figures who he blamed for "letting down" vulnerable children.
He argued Coun Box would bear "ultimate responsibility" if the service's Ofsted rating did not improve.
Coun Ayre said: "The lack of strategic leadership is unforgivable, as are a number of decisions taken by those at the very top:
"Decisions like paying off senior council officers hundreds of thousands of pounds in exit packages who have so badly let us down; decisions like taking so long to replace them, and also underfunding the service as a whole, only to find the money after the (Ofsted) report comes out.
"The leader will not have the confidence of the full council if he does not deliver the improvements so desperately needed."
Coun Box did not speak during the debate, but voted with all Labour councillors present in backing Coun Ayre's amendment. However, he had earlier been involved in several angry exchanges with the Tory leader.
When Coun Ahmed at one point told him "you've got nothing left to offer", the council leader responded, "What have you offered in the last five years? Nothing."