Tory grandees have raised the possibility of a change in the rules governing challenges to the party leader.
Under the current system, a move against the leader can only be brought once in a 12-month period.
Theresa May saw off a bid to oust her last December and so would not expect to face the risk of another possible attempt to topple her until the end of the year.
However, two former chairmen of the 1922 Committee of backbench Tory MPs said rules could be changed.
Writing in the Sunday Telegraph, Lord Spicer and Lord Hamilton of Epsom said the 12-month rule on no confidence votes had been “interpreted as being immovable”.
“It is reported that in order to change this rule the whole Conservative Party constitution must be opened, a National Convention called and even that a petition of 10,000 members is required. This is not the case,” they said.
Insisting that party rules were “not the master”, they added: “Conservative MPs are responsible for their party. If they wish to change these rules there is nothing standing in their way.”
Current chairman of the 1922 Committee, Sir Graham Brady, told the paper: “It is my understanding that the rules could in future be changed by the agreement of the 1922 executive.”
He added that it was “less certain that it would be possible to change the rules during the current period of grace which was initiated with the triggering of a confidence vote on December 12 last year”.
It was launched after Sir Graham received letters from 15% of Conservative MPs writing a letter asking for a vote.
Mrs May won that ballot by 200 votes to 117, but following the delay of Brexit to October 31 a number of Tory Eurosceptics have raised questions about her future as Prime Minister.
Former Conservative Party chairman Lord Tebbit also warned that “scores” of Conservative councillors could be “thrown out” in next month’s local elections because of Mrs May’s failure to deliver Brexit and said a new Prime Minister was needed.
Writing in the Sunday Telegraph, he said: “I can only urge all my Conservatives in the Commons to act to save our party and the country from the growing dangers of a failure to honour their pledges to deliver Brexit without strings.
“The prerequisite for that is the removal of Mrs May from No 10 to make way for a genuine Conservative.”
Fellow former party chairman Sir Patrick McLoughlin warned against handing the keys to No10 to a hard Brexiteer.
“Defining ourselves as the Brexit party, pursuing the hardest form of Brexit with a parliament that will not deliver it, is a recipe for paralysis in government and suicide with the electorate,” he said, in an article for The Sunday Times.
“We are the Conservative Party, not the Vote Leave Party.”
Meanwhile, the Sunday Telegraph reported that an Electoral Calculus poll of polls showed the Tories could lose 59 seats at a general election, and Labour would become the biggest party in the Commons.