A bankruptcy judge has dealt a big blow to Aéropostale Inc.’s bid to survive chapter 11, refusing to rein in the bidding rights of Sycamore Partners, a former big backer and now major critic of the retailer.

Judge Sean Lane, in a decision signed Thursday but not made public until Friday afternoon, said Sycamore is entitled to wield its $151 million loan as currency at the bankruptcy auction of the retail chain, a so-called credit-bid that gives it an advantage in the competition.

The...