It's been 10 days since the couple have answered police questions on "things that we believe only they would know about," Kansas City police spokesman Steve Young said.
The child's mother, Deborah Bradley, has given television interviews since then, including at least two in which she said she had been drinking the night Lisa disappeared and may have blacked out.
"Our focus has always been and remains to find this girl," Young said. "And as I said before, we strongly believe that their complete cooperation and communication with detectives is critical for that to happen."
Bradley and the child's father, Jeremy Irwin, said he arrived home from a night shift Oct. 4 to find the front door unlocked, the house lights on, a window tampered with and the baby gone. Police, FBI agents, officers from area law enforcement agencies and even the Missouri National Guard, have searched the family's home, neighborhood, nearby wooded areas, a landfill and abandoned homes. Police have refused to discuss any evidence gathered in the searches, saying only that they remain without a suspect.
On Tuesday, police crime scene technicians and detectives went over a wooded area east of the family's home.
As the searches continue without any arrests, attention has turned to Bradley and her network interviews. She told NBC that she was drunk the night she last saw her baby and that she did not see the baby after putting her to bed at about 6:40 p.m. -- roughly four hours earlier than the time she originally gave police. She didn't explain the difference.
Her lawyer, Joe Tacopina, did not return messages seeking comment Tuesday. On Monday, he said the parents were done giving media interviews, but he insisted they were innocent.
"I don't recall in recent history anyone under this umbrella of suspicion be so open and forthright, warts and all, regarding the events. Because they have nothing to hide," Tacopina said.
He added later that Bradley's admissions about drinking "goes to her credibility."
"That's something she was willing to tell the truth about even if it didn't make her look good because she's got nothing to hide," he said.
Jeff Lanza, a retired FBI special agent, said the manner in which the child's disappearance has unfolded publicly has been "bizarre" and may have reduced public support for the parents.
"The fact that they've been on national TV so much ... the fact that they've been out there so much and then publicly changing their story, or she is publicly changing the story, is very surprising," Lanza said.
"On the one hand, they're trying to keep the story in the news, but being interviewed on national TV by seasoned interviewers ... you probably should be shying away from doing something like that," he said. "You're trying to gain public support, and you could be detracting from public support."
Kansas City residents in and around the family's neighborhood attended prayer vigils, fanned out in searches and handed out fliers featuring a picture of Lisa after she disappeared.
But while police continue their hunt, many neighbors, weary of the steady media presence on their quiet winding road, have stopped talking to reporters. A small group patrolled the street over the weekend but didn't want to talk to the media.
Joe Robinson, 53, of Kansas City, has been handing out fliers to the steady stream of gawkers who slowly drive by the family's home, where well-wishers have placed stuffed animals and handmade signs expressing love and concern for the missing baby.
Robinson said he has been trying to drum up community support but without much success.
"People want to accuse people, and nobody wants to get involved," Robinson said. "It makes me cry. ... When you hear somebody's missing somewhere, the community needs to get together."
