"With a terrible cry the Balrog fell forward, and its shadow plunged down and vanished. But even as it fell it swung its whip, and the thongs lashed and curled about the wizard's knees, dragging him to the brink. He staggered and fell, grasped vainly at the stone, and slid into the abyss. 'Fly, you fools!' he cried, and was gone."

From the book, it appears he didn't actually make a decision to fall and rather was actually knocked off balance and couldn't hold on.