12:25 PM PST -- The Houston family says, "Bobbi Kristina is fighting for her life and is surrounded by immediate family. As her father already stated, we are asking you to honor our request for privacy during this difficult time."
Bobbi Kristina -- who was revived from death over the weekend -- is now doing significantly better ... TMZ has learned, but it's still touch and go.
Sources connected with the family tell us ... doctors performed tests Monday morning and determined the swelling on her brain has gone down. In addition, she has been able to "move her eyes" ... all important signs.
Perhaps most important ... we're told the oxygen levels in her brain have increased significantly -- 4 times better than Sunday.
But the family has been told ... because Bobbi Kristina was deprived of oxygen for anywhere between 2 to 5 minutes while she was submerged in a tub, doctors fear neurological damage.