why could Supergirl not be able to breathe in space?
Because no-one can...there's no air.
She can't breathe in space unless she stores solar energy and holds her breath.
In the modern version of Superman (in the comics at least until the next version), Superman's sight, stamina and breath powers have been substantially reduced, and the character was also shown as requiring an oxygen mask for prolonged travel in space or underwater.
The same would apply to Supergirl.
I suspect though you are asking why Supergirl became unconscious and had to be rescued.
Well, she'd just lifted the 1 million ton Fort Rozz into orbit and beyond...that would have expended a...ahem...superhuman amount of energy which would have depleted her reserves. Plus the air is essentially too thin to breathe over 10,000 meters and Earth orbit is substantially higher than that.
So, she ran out of energy and breath and fell unconscious.