They had been granted legal aid and were due to put their case before a judge on Friday but have now been advised that their case was not strong enough.
A legal expert told them that if they lost their case, they could incur huge costs.
Campaigners started the battle after Calderdale councillors recommended the Victorian primary school should close at Christmas - a move which was confirmed after a public inquiry by Schools Adjudicator Dr Alan Billings in July.
It is a year since inspectors branded the school as failing and placed it in special measures for the second time.
A spokesman for Irwin Mitchell Solicitors today said "Despite their deep concerns, Mixenden parents have decided to stand back to see what the local authority does to provide not only for the pupils directly affected by the closure but those who will be needing a primary school place on the estate in the near future.
"At the forefront of their minds has been the fact that the school is now due to close in a matter of weeks. They have concluded that the steps taken by the local authority toward closure have taken their toll on the school so that it is now too late to prevent the temporary annex proposal from going ahead, however short-sighted and ill-planned it may be."
Calderdale Council said it would not pursue legal costs against parents who sought a judicial review on the closure.
The council said solicitors acting on the groups' behalf informed it they were withdrawing their challenge.
Caroline Gruen, Calderdale's education director, said the council could make a claim against the parents to recoup costs.
She said: "The decision not to claim costs on this occasion does not set a precedent."
But Jackie Maude, whose twin five-year-old daughters, Rosey and Ebony, attend the school, said: "Our lawyers have advised us to scrap our challenge but I'm not happy about the decision.
"They told us that we would have a slim chance of winning, but to be told we have to abandon our case at this late stage has knocked us all for six."
She said a meeting with the headteacher and members of the council at Mixenden School was planned this week.
Russell Noble, secretary of the Mixenden Residents' Association said any action taken by the parents' association would have their "tacit support".
Clem Rushworth, chairman of governors, said he was shocked at the lateness of the withdrawal but said he was relieved that an end to the confusion was in sight.
"If this is the end of it, and parents decide that the campaign is to be stopped, from my perspective, then at least it removes the instability which has been hanging over the school for some time. It's been difficult to run in these circumstances," he said.
"For my part now, I must continue working towards closing this school on the 31st of December, I don't have any other option."