How long can a hang glider stay up?

As long as you can find lift, you can stay up as long as you want.

Thermal lift is obviously dependent on heat so it's limited to day-light hours but ridge-lift can continue on indefinitely. Ridge-lift is when the wind blows up the side of a hillside and deflects the air vertically - the hang glider gets in that and up it goes! A long time ago a pilot in Hawaii stayed airborne 30 hours by riding the sea-breeze coming in. He would adjust his speed and hover close to the ground and people on the ground would hand him drinks and something to eat.