The scene in which Finney writes that Tom does not permit himself to look down illustrates his lack of foresight before going out onto the ledge. His thinking clouded by his overriding ambition, Tom has one thought: Retrieve the yellow sheet. Therefore, he ventures out onto the ledge without considering any danger or consequences:
It was hard for him to understand that he actually had to abandon it--it was ridiculous--and he bagan to curse....
For many seconds he believed he was going to abandon the yellow sheet, that there was nothing else to do....But just the same, and he couldn't escape the thought, this and other independent projects, some already done and others planned for the future, would gradually mark him out from the score of other young men in his company....And he knew he was going out there is the darkness, after the yellow sheet fifteen feet beyond his reach.....
To simply go out and get his paper was an easy task--he could be back here with it in less than two minutes--and he knew he was not deceiving himself....On a sudden impulse, he got to his feet...In the back of his mind he knew he'd better hurry and get this over with before he thought too much, and at the window he didn't allow himself to hesitate.
Once on the ledge, fear "stirred in his stomach," but he he moves, "not allowing himself time to think. Tom knows that if he looks down, his terror may shake him, and he may lose his balance and fall to his death. In addition, Tom's refusal to allow himself to look down is symbolic of his single focus on his ambitions. For, it is not until he considers his plight that he considers how meaningless his death would be--empty, like the contents of his pockets. It is not until he does look down that he realizes his love for his wife Clare.
Well, have a think about where Tom actually is and what he is doing? I don't know if you suffer from vertigo (the fear of heights), but to those of us who do, looking down if you are clinging on to the side of a building high up in the air with nothing to stop you falling to your doom would be terrifying. It is clear from the text that Tom recognises his desperate situation - he feels the fear stirring in his stomach, but he is so fixated on achieving his goal that he carries on "by not allowing himself to think." Note how his progress is described:
He could hear the buttons of his jacket scraping steadily along the rough bricks and feel them catch momentarily, tugging a little, at each mortared crack. He simply did not permit himself to look down, though the compulsion to do so never left him; nor did he allow himself actually to think. Mechanically - right foot, left foot, over and again - he shuffled along crabwise, watching the projecting wall ahead loom steadily closer.
Here we see that Tom is only able to do what he is doing by being incredibly strict with himself and not allowing himself to either look down or to think about his situation. The word "mechanically" accurately reflects his actions - he is only able to proceed if he acts like a robot. Thinking and feeling like a human being would spell certain doom.
To answer this question, think about where Tom is and think about your own likely reactions if you were where he is. I think you will see why he didn't look down.
If I were way high up on the narrow little ledge of a building I would be scared senseless. If I looked down, then I would be even more afraid. If I just looked at the building in front of me, I could pretend that the ground was two feet below or something and not be so scared. But if I looked down, I would see how far I was about to fall and I would think about how dead I was about to be.
To me, that's why Tom doesn't look down.