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"failure to accept" is correct and usable in written English.
You can use it when referring to an individual's or group's unwillingness or refusal to acknowledge something. For example, "The failure to accept that climate change is real has put the planet in danger."
Exact(60)
This layer is more psychological rather than anything else, due to grasping onto the reality of something and the acceptance or failure to accept it.
His failure to accept the full recommendations is unfair and regrettable, he says.
And the institutional failure to accept changes means that confidence in the currency is declining.
We acknowledge that our failure to accept responsibility for apartheid has inhibited reconciliation and transformation".
Four months later, the failure to accept that price begins to seem tragic.
He may have succeeded, only to find himself on fresh charges of weak departmental leadership and failure to accept responsibility".
(His failure to accept McCain's imaginative proposal for a series of unmediated joint appearances was among them).
I'm hoping you mean this one, written by @graemesmith1978, about Michael Gove's "failure to accept the individual nature of pupils".
A greater part was devoted to China's suppression of its currency and its failure to accept global obligations.
But the justices surely understood that their failure to accept the case would further undermine the rule of law.
FISH SCORES FRANCE ON DEBT.; Says Failure to Accept $40,000,000 Offer Would Be Bad Faith.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com