The network has filmed only one sting operation so far this year, compared with seven in 2006. In several ways, the high ratings for “Predator” have come at a high price for NBC. Some advertisers say they are wary of being associated with the show’s content, in which men lured to a house by the promise of a sexual encounter are instead surprised by Mr. Hansen and then arrested.

Critics have also raised ethics questions about the series because NBC coordinates the investigations with a private watchdog group and local police departments. And two lawsuits are pending against the network, one by a former producer and another by the sister of a man who committed suicide as police officers approached his house, accompanied by NBC camera crews.