Senior Tories have voted against plans to change party rules to get rid of Theresa May within weeks.
The influential 1922 Committee rejected the plans to allow a vote on Mrs May’s leadership as early as June - reportedly by a narrow margin of nine votes to seven.
It now means that Prime Minister is safe until December - but she is being pressured to make it clearer when she intends to depart.
The committee of backbenchers demanded "clarity" over what she will do if her EU withdrawal deal fails, while the chair of the 1922 Committee, Sir Graham Brady, said it would be "a surprising response" if Mrs May suggested she might stay on as late as December this year.
Sir Graham made clear he remained ready to convey MPs' concerns about her leadership to Mrs May.
And he asked the Prime Minister to set out a "timetable and schedule" for her departure in the case that her Withdrawal Agreement fails to secure parliamentary approval.
Asked on ITV News whether Mrs May might reply that she planned to stay on until December, Sir Graham said: "I think that would be a surprising response.
"We have communicated our request, which is in very clear terms, for proper clarity about her plans for departure should the Withdrawal Agreement not be approved.
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"We need to hear her response to that and colleagues will of course form their own judgement when they receive that response.”
Mrs May said in March she would step down once the Agreement was ratified, in order to hand over to a new prime minister to conduct further talks with the EU on a future trade deal.
But the offer of self-sacrifice failed to win over enough rebels to avoid a third crushing defeat in the Commons, forcing Mrs May to accept a delay to Brexit until October 31 and sparking calls for her to name a date for her departure.
One member of the 1922 executive, former deputy speaker Nigel Evans, called publicly for Mrs May to go "as soon as possible”.
But other members were reported to have pushed back, questioning what a fresh leadership contest at the current time would achieve.
Cross-party talks on a Brexit compromise were continuing on Thursday, with time growing perilously short to find a deal which could halt next month's European elections.
Despite expressions of frustration from both sides in recent days, talks on the environmental aspects of the deal were due to take place between Environment Secretary Michael Gove and his Labour shadow Sue Hayman.
Mrs May is running out of time to find a compromise which would clinch ratification of her Brexit deal in time to cancel the May 23 polls.
In order to meet the deadline, the Withdrawal Agreement Bill could be tabled in the Commons as early as next week, even if a deal with Labour has not been reached.
But the Government is wary of moving too soon, as defeat for the Bill would force Mrs May to bring the parliamentary session to an end and schedule a new Queen's Speech, leading to additional delay.