THE “Free the Beatrice” effort appears to have failed. An insider tells Page Six that the West Village hot spot, which has been shuttered since April, is up for a liquor-license renewal at the beginning of next year — and has almost no chance of getting it. “Neighbors are still campaigning against the club, and they have the support of the city,” says our source. “To reopen, they’d have to pay $23,000 in fines, install a fire door that matches the period exterior of the building, and put in a sprinkler system. They’re not gonna do it, since they know the license will be revoked.” Neighbors had also complained to authorities about late-night traffic into an apartment upstairs in the front of the building the club used as a VIP lounge. When one resident, who lived above the dance floor in the rear, complained about noise, owner Paul Sevigny let him move, rent free, into that front apartment, ending the complaints. Sevigny could not be reached for comment.