People for the Ethical Treatment of Animals asked the company to begin providing quarterly reports on its suppliers' development of "controlled atmosphere killing," or CAK, which euthanizes chickens by gradually replacing their oxygen with inert gases.
Most slaughterhouses stun the chickens with electricity, which PETA claims often leaves the birds still aware when their throats are slit and their feathers are removed in boiling water.
The proposal received less than 5 percent of shareholder votes, Applebee's officials said during the company's annual meeting.
Last year, a similar proposal failed with less than 6 percent of the vote.
Applebee's says the technology, which is used in Europe, is still unproven but that the company will continue to monitor its progress.
Matt Prescott, a campaign coordinator for PETA, said the group will likely return next year with the same suggestion for Applebee's. PETA has proposed the change to numerous restaurant and food-processing companies, including Wendy's, Hormel Foods Corp., ConAgra and McDonald's.
"Applebee's shareholders have had a chance to understand the benefits CAK would bring to the company," Prescott said after the meeting.
Shareholders also voted to add Rogelio Rebolledo, president and chief executive of Pepsi Bottling Group Mexico, to the board of directors.
Lloyd Hill, Applebee's chairman and chief executive, told shareholders unhappy with last year's shrinking profit that the chain of 1,839 restaurants worldwide planned to revamp its marketing effort and change its menu more often.
"While we have no control over gas prices ... we are focusing on the things we can control, which is our food," said Hill, who plans to step down as chief executive this summer, likely to be replaced by Dave Goebel, the company's president.