Bobbi Kristina, the only daughter of the late Whitney Houston and Bobby Brown, remains hospitalized in the intensive care unit after she was found face down in a filled bathtub at her Georgia home. The 21-year-old was placed in a medically induced coma late Saturday night because of swelling in her brain and was also hooked up to a ventilator.

According to CNN, Brown's eyes opened and closed on Monday - the first sign of a slight improvement - but doctors warned the family not to read too much into it. Because Brown has been in a coma for the past few days, doctors don't know the status of her brain's function. Tests can't be performed until Brown is fully taken out of the coma.

Another family source told the site that doctors wanted to take Brown off the sedatives but decided against it. Reportedly, she also had a few seizures. CNN contributor Nischelle Turner reported that an insider close to the Houston/Brown family revealed that the aspiring actress and singer is in "really bad shape" and everyone is "hoping for the best" but "preparing for the worst."

A source previously told People magazine that it would be a miracle if Brown pulled through. On Sunday, TMZ reported that the family had started discussing funeral arrangements. It's not clear what led to Brown's unconsciousness.

Police revealed that she was home with at least two other people - her husband Nick Gordon and a friend - when the incident happened. Her home was searched over the weekend for drugs but, at fist, police said they didn't find anything.

According to TMZ, a second search was conducted Monday morning and this time officers did allegedly find drugs in the house. A police official told the site that the initial search was only for things "out in the open," whereas the second search was more "thorough."   

The family issued a brief statement to CBS Atlanta saying that Brown was "fighting for her life" and they were continuing to pray. 

"Bobbi Kristina is fighting for her life and is surrounded by immediate family," the statement read. "We are asking you to honor our request for privacy during this difficult time. Thank you for your prayers, well wishes, and we greatly appreciate your continued support."