But the camp, at Arthur's Wood in the Bollin Valley, was given a seven-day stay of execution by the Court of Appeal in London.
The three judges, who decided two-to-one that the activists should be moved on, have given the protesters' legal team time to take another appeal to the House of Lords.
"We're optimistic," said Green Party legal advisor Chris Maile yesterday.
"We will get our leave to appeal to the Lords. I have no hesitation in saying that.
"In our view we're right and we're going to take it to the extreme."
If the treetop protesters win a long enough stay of execution, proposed tree felling would have to be postponed until September because of the nesting season.
The activists have been in tunnels and tree houses on the National Trust-owned woodland outside the runway perimeter for the more than six months - and have since taken over airport-owned woodland further along the valley.
Aviation rules say it must be cut back because of the new radar line created by the proposed runway.
But eco-activists say the National Trust should not allow trees to be felled for commercial gain.
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