There was only one choice, really. Yes, she was terrified of the heights, and kept her eyes averted from the drop so she wouldn't pass out from fear, but she was also loyal to her duty. There would be no way of capturing this prisoner if she were dead, but as long as she was with him, then she could find a way to get help.
"All right! I'll help you!" Her eyes accidentally strayed down below and she quickly shut her eyes. "Now pull me back! I said I'd help you, damn it!"