The parents of missing 6-year-old Isabel Celis begged for her return in their first live television interview Thursday, and they said they fear police may be wasting time focusing the investigation on them.

Becky Celis said on NBC’s “Today Show” that Isabel is a “girly girl” who loves to put on makeup and paint her nails, but she also likes playing outside in the dirt with her brothers. Becky and Sergio Celis told police that Isabel vanished from her bedroom in their Tucson home after she was put to sleep around 11:00 p.m. on April 20. She was gone when Sergio went to wake her the next morning.

“I was asking her if she was hungry,” Sergio said, describing the last time he saw Isabel, “and she just had that little sleepy look as she was walking by, and she just said, ‘No, daddy. I’m tired.’ She was just walking by. She is so full of life and she is just so wonderful.”

Becky said the level of scrutiny the parents have faced is “nothing we can’t handle,” and they believe police are doing everything they can to solve the case. However, Sergio said it can still be difficult because detectives are only able to share limited information with them and “they keep us at bay.”

“We understand that they can’t bring false hope, but at the same time, you know, we’re desperate. We’re desperate in finding out information. We’re extremely frustrated that it’s taking so long,” Sergio said. “…We do feel sometimes that they’re wasting time with us even though we know we have to be under, you know, scrutiny, absolutely understandable.”

Isabel’s parents urged people to continue praying for their “beautiful baby girl” to be brought back home, which they called “her favorite place in the world.”

Tucson police confirmed to HLN Thursday that both parents have taken polygraph tests, but they would not comment on the results. “Nancy Grace” producer Greg Overzat was on the scene Wednesday afternoon when detectives brought the parents and Isabel’s older brother back into the house separately.

Lt. Fabian Pacheco said at a Wednesday press briefing that the walkthroughs with individual family members are just a method investigators use, they were done with the family’s consent and they do not indicate a focus on anyone in particular. According to Pacheco, police have received about 500 tips in the case so far and they are following up on all of them.

For the latest news on the Isabel Celis case, watch Nancy Grace Thursday at 8 p.m. & 10 p.m. ET on HLN or go to www.HLNtv.com.