The family of a Sagaponack woman who's been missing for 12 days is asking the public for help, saying they haven't lost faith in her safe return.

Lilia Aucapina, 40, who also goes by Lilia Esperanza, was last seen about 9 a.m. on Oct. 10, walking west on Montauk Highway in Wainscott. She was reported missing by family members about 12 hours later.

"Our family's in shock because she's a good woman, and we'd never expected that she wouldn't come home. We have no explanation for it," said Aucapina's brother, Victor Parra, speaking in Spanish through a translator Wednesday afternoon.

StoryPolice: Hamptons woman, 40, still missing StoryCops trying to locate missing Hamptons woman

The family has distributed fliers with her picture in hopes that someone will come forward with information.

"Right now, we believe that she's safe, and that she's alive," Maria Duchi said of her aunt, who has a daughter, 14, and son, 21. "We have faith."

The day she disappeared, police said Aucapina had an argument with her estranged husband, Carlos Aucapina, in the parking lot of the Meeting House Lane Medical Practice in Wainscott. The two are getting a divorce, police said.

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Carlos Aucapina, 50, was later arrested, accused of violating a protection order his wife had obtained, police said.

Southampton Town police said no arrests have been made in connection with the disappearance, but they have not ruled anyone out as a suspect.

Police have searched the Southampton and East Hampton areas, and sent out a recorded message to South Fork residents asking for help finding Lilia Aucapina. Town police Lt. Susan C. Ralph renewed that call Wednesday at the news conference at police headquarters.

"We are asking for any and all assistance from the public. This is not only a sister, a daughter, but a mother who's missing," she said.

Aucapina is originally from Ecuador. She is described as 5 feet, 3 inches tall, 130 pounds, with medium-length black hair and brown eyes. She was last seen with her hair pulled up, and wearing blue jeans, brown boots and a black winter jacket.

Police are asking anyone with information regarding her whereabouts to call them at 631-702-2230 or 631-728-3400.