bobbi-kristina-brown*Bobbi Kristina Brown’s condition may be a bit better than it was earlier this week, but according to a source closely connected to the situation, her fate may be in the hands of her family.

“It’s now a matter of when the family wants to let go and accept that she’s pretty much not going to make it,” the source told FOX411, while stating that Bobbi Kristina’s doctors have expressed that there is little they can do. “They’ve left it up to the family as to how long they want to keep her alive.”

The latest news on the daughter of the late Whitney Houston comes amid reports earlier this week that her situation was particularly weak and her brain function was alarmingly “low” after being placed in a medically induced coma. Despite the circumstances, Page Six reports that Bobbi Kristina’s father, singer Bobby Brown, refuses to acknowledge the worst-case scenario as he remains hopeful and encourages others to stay uplifted.

On a positive note, a source connected to the Houston family mentioned Bobbi Kristina’s condition has actually improved somewhat. As a result the 21-year-old’s situation looks better than it was previously.

Speaking with an attorney for Bobby Brown late Tuesday, FOX411 says an investigation is currently being held regarding the events leading to Bobbi Kristina’s hospitalization. The inquiry comes amid reports from media sources, which reveal that Bobbi Kristina has never been married to Nick Gordon.

On Saturday, Bobbi Kristina was rushed to a hospital in northern Atlanta after she was found unresponsive in a bathtub at her Roswell, Ga., home. Bobbi Kristina was later relocated to another hospital. Details as to when and why she was transferred are unclear. Just last Thursday, reports surfaced of Bobbi Kristina’s plans to record a tribute album to her mother Whitney Houston with her father this year.

“We continue to request privacy in this matter,” Bobby Brown said in a statement. “Please allow for our family to deal with this matter and give Bobbi Kristina the love and support she needs at this time,” Bobby Brown added in a statement.

A family statement released Monday echoed Bobby Brown’s request for privacy, saying, “Bobbi Kristina is fighting for her life and is surrounded by immediate family. We are asking you to honor our request for privacy during this difficult time.”