"In his mind, she's going to pull through," a source tells PEOPLE

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While daughter Bobbi Kristina Brown remains unconscious and unresponsive in the hospital, Bobby Brown is maintaining hope that she’ll make it through.

“He’s going to give her every chance to fight for her life,” a source tells PEOPLE. “He’s trying to keep as positive as possible.”

The daughter of the late Whitney Houston and Bobby, Bobbi Kristina, 21, was found facedown and unconscious in her bathtub Jan. 31, before being rushed to North Fulton Hospital in Roswell, Georgia.

Bobbi Kristina has since been moved to Emory University Hospital in Atlanta, where she remains on life support. Her family, including grandmother Cissy Houston, have stayed close to her bedside since she entered the hospital.

“I think they’re going to try to wait and see [what happens],” the source says, adding of Brown: “In his mind, she’s going to pull through – she’s a fighter, and she’s going to pull through. I think he’s going to hold out as long as he possibly can.”

As for Bobbi Kristina’s current condition, a Brown family member told PEOPLE Sunday morning there was “no change.”

Wednesday will mark the three-year anniversary of Bobbi Kristina’s mother’s death. Houston was found unconscious in a hotel bathroom in Los Angeles on Feb. 11, 2012; her death was ruled an accidental drowning, and reports found cocaine, marijuana, Xanax, Benadryl and other medication in her system.

Meanwhile, authorities have launched an investigation into Bobbi Kristina’s drowning. Her boyfriend Nick Gordon is reportedly at the center of the investigation.

With reporting by STEVE HELLING

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