The Court of Appeal has upheld the High Court's refusal to grant a judicial review into Relationships and Sex Education (RSE).
The legal challenge was brought by the Let Kids Be Kids Coalition (LKBK), which is concerned that children are being taught inappropriate sexual material and transgender ideology in RSE lessons.
The RSE curriculum became mandatory for schools last September but they were given until summer 2021 to implement it because of the pandemic.
A controversial point has been the right of parents to withdraw their children, with no right of withdrawal at all from relationships lessons.
The Court of Appeal sided with the High Court this week on the grounds that the claim was brought "out of time".
LKBK said it was "deeply disappointed" by the Court of Appeal's decision, and disagrees with the judgment that it was "out of time".
"The judge had the option to exercise discretion and to extend the time for bringing the claim, but declined to exercise this discretion," said LKBK.
The coalition said it would continue to challenge RSE and was "reviewing next steps".
"Clearly we are deeply disappointed that our efforts in the court system have been stymied. The seriously important issues raised were never even addressed in court. Rather procedural abstractions were used to sideline the process," said LKBK founder and Chairman Charlie Colchester.
"In the light of this we have to take stock. The most important decision is that we cannot let the children of this country down, so we will continue in a number of different ways both in court and outside. This is just the end of a phase.
"Intensive discussions are continuing with a wide range of possible allies across the whole multi-faith community."
He added: "There is an increasing groundswell of real concern amongst parents, schools and pupils, as the reality of what the Government's new RSE curriculum is sinks in. LKBK is receiving more and more appeals for help."