Deputy Labour leader Tom Watson is facing a fresh bid to oust him by abolishing his post.
An initial move was made at the party’s National Executive Committee (NEC) meeting on Friday but it failed to get the two-thirds majority needed.
A further attempt will be made on Saturday at the party’s conference.
It is understood that it was proposed by Jon Lansman, founder of Labour grassroots group Momentum.
The campaign group was set up to support Jeremy Corbyn’s leadership of the Labour Party.
Mr Watson has been at odds with Mr Corbyn over Labour’s stance on Brexit.
He wants another public vote on the UK’s membership of the EU before any general election, but Mr Corbyn has said an election should come first.
The party leader has refused to say which side he might back in a future Brexit referendum under a Labour government.
A Momentum source told the BBC: “We just can’t afford to go into an election with a deputy leader set on wrecking Labour’s chances.
“Labour members overwhelmingly want a deputy leadership election, but our outdated rulebook won’t let it happen.”
Neither Mr Corbyn or Mr Watson were at Friday’s NEC meeting.
A senior Labour source said: “Tom had given his apologies to the NEC… as he had to look after his children.
“Usually when you disagree within parties on issues like taking a remain stance on Brexit, you have a debate. Seems that in Jeremy Corbyn’s Labour Party they’d rather abolish you than debate with you.”
The position of deputy leader has existed within the Labour Party, which was formed in 1900, for nearly a century.
John Robert Clynes became the first deputy leader in 1922, and the position has since been held by prominent Labour figures including John Prescott and Harriet Harman.
The NEC, Labour’s governing body, will vote again on abolishing Mr Watson’s post at the party’s annual conference at 10:00 BST on Saturday.
Sources told BBC political editor Laura Kuenssberg they expected the vote to be passed.
There will then be a vote on the conference floor in the afternoon, where it is expected the bid will be approved, ousting Mr Watson.
BBC political reporter Jessica Parker said Mr Watson’s supporters were “not overly optimistic” that he will win Saturday’s vote.
Labour MP Wes Streeting said in a Twitter post the push to oust Mr Watson “isn’t just outrageous, it’s self destructive”.
“Labour Conference this week needs to put the Party on a general election footing – talking to the country about our vision for Britain,” he wrote.
Labour MP Jess Phillips tweeted: “Wish that we could just stop pretending & say what we think… There’s a desperate attempt to control & expel anyone who has an independent thought.
“I’m so sick of pretending just say you hate Tom Watson just be honest.”
And former Labour leader Ed Miliband tweeted that those who had come up with the idea to abolish the deputy leader post had “taken leave of their senses”.