The FBI has searched a suburban landfill for the second time this week, in an increasingly distressing investigation into the disappearance of 10-month-old Lisa Irwin.

Lisa is believed to have disappeared from her crib sometime late Monday night or early Tuesday morning.

FBI spokeswoman Bridget Patton told ABC News that investigators spent two hours searching the Deffenbaugh Industries landfill in the Kansas City suburb of Shawnee. She confirmed that the search was related to the missing infant's case, but did not provide any further details.

The same landfill was searched on Tuesday, the day Lisa Irwin was first reported missing.

Relations between Kansas City police and the 10-month-old infant's parents, Jeremy Irwin and Deborah Bradley, became strained late this week -- with investigators beginning to paint a picture of the young couple as being uncooperative and unreliable.

Bradley and Irwin went on the Today show Friday to discuss the ongoing investigation to find their daughter -- which has turned up few leads and no official suspects.

Matt Lauer opened the interview by telling Lisa's parents that in the numerous missing children cases he has covered, he has rarely seen the police make a statement that the child's parents are uncooperative -- an accusation Kansas City Police aimed at Irwin and Bradley, an unmarried couple who each have children from previous relationships who live with them.

In a press conference Thursday evening, Capt. Steve Young said Lisa's parents were no longer cooperating, which may or may not have been a misinterpretation of their request for a break from being questioned.

We were at the station yesterday being interviewed again, and I just had reached my boiling point and asked them, 'Guys, I can't do this anymore today, I need a break, [and] I can't answer any more questions,''' Irwin, 28, told Lauer. The next thing we knew was the press conference yesterday. We want to make sure that we tell everybody that we're still cooperating, we're still talking to police, [and] we're still doing everything we can to try to find Lisa and bring her back home.''

Only Bradley has taken a polygraph test -- which she said she volunteered to do. Police told her she failed, but Bradley did not recall which questions she was believed to have answered falsely.

Irwin told Lauer he had not been asked to take a lie detector test, which prompted the host to ask if he would be willing to do so. Irwin gave an affirmative, if somewhat vague, response.

I'd be willing to do whatever it takes to bring my daughter Lisa home where she belongs, he said.

Lauer asked Bradley if she believed the police calling [her] out was an attempt to pit husband and wife against each other.

Bradley answered after a brief hesitation. Possibly, she said. She later added, our concern is to find Lisa and bring her home...I don't care what we have to go through to get it.

The parents addressed the situation on Good Morning America as well.

From the start when they've questioned me, once I couldn't fill in gaps, it turned into 'You did it, you did it,' Bradley told GMA Friday. They took a picture down from the table and said, 'Look at your baby! And do what's right for her!' I kept saying I don't know ... I just sat there. I didn't even ask to leave. I just let them keep asking questions.

Suspicion almost always falls heavily on the parents, especially when it's young kids, David Finkelhor, director of the Crimes Against Children Research Center based at the University of New Hampshire, told ABC News.

For a parent who has been a victim of a true stranger abduction, this is devastating. You're dealing with the loss of a child, and police are considering you as one of the prime suspects, Finkelhor said. You can get non-cooperative because the family is feeling mistreated by police.

The Kansas City Star reports that police took down the command post, which has been used as central headquarters for the investigation, Thursday night. But Sgt. Stacey Graves, a Kansas City police spokeswoman, said the decision had nothing to do with the parents' level of cooperation.

We used that location to organize a lot of the big geographic searches, Graves told the Star. But we feel that location is no longer necessary, adding, We are continuing the investigation.

On Wednesday, Jeremy Irwin and Deborah Bradley pleaded for their daughter's safe return during a press conference at a police command center near their home.

Please drop her off anywhere, Jeremy Irwin is quoted as saying by The Associated Press.

We just want our baby back, Deborah Bradley said, while clutching a Barney doll that presumably belonged to Lisa.

Kansas City police Capt. Steve Young told ABC's Good Morning America Wednesday that police are not ruling out any possibilities -- including the involvement of Lisa's parents -- but that neither her mother or father were a suspect and that both had been fully cooperative with the investigation.

Detectives are looking at every possible angle, Young told MSNBC. All we know is that there should've been a 10-month-old in that house and we are doing everything we can to find the kid...We've received several tips and we certainly encourage people to call, but we also need information that is specific to the case.

According to Lisa's parents, she was last seen at around 10 p.m. Monday night when her mother put her to sleep, and her father noticed she was missing when he returned home from work at around 4 a.m.

Police intially suspected an intruder but have not yet determined the location of a forced entry. There was no information as to whether the child's room included an operative baby monitor, Sgt. Stacey Graves told the Kansas City Star.

One neighbor interviewed said he had seen a man carrying a baby near the Irwin's home at 2 a.m. Tuesday, but police spokesman Darin Snapp told MSNBC that lead went nowhere.

Two other children, sons from Lisa's parents' previous relationships, live in the home. Both are boys aged ten or younger.

Lisa Irwin has blue eyes and blond hair. She is 30 inches tall and weighs 26 to 30 pounds. The baby was last seen wearing purple shorts and a purple shirt with white kittens on it. She has a cold with a cough, a small bug bite under her left ear, a beauty mark on her outer right thigh, and two bottom teeth.

An Amber Alert for Lisa was issued on Tuesday but was called off on Wednesday. Police indicated the decision was a formality, as the alerts function to raise awarness of a missing child at the beginning of the investigation.

Although the investigation and search for Lisa Irwin continue, an active Amber Alert is no longer necessary in this case, CNN reports a police spokesperson saying on Wednesday.

Police are urging people with any possible information that could lead to Lisa's whereabouts to call TIPS Hotline at 816-474-8477, or 911.

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