Hello Mr. V.,
I was just curious.. How did you approach her the second time? Did you start another conversation with her first? Or did you just kind of throw it out there "Hey, want to hang out sometime?" If you did it the second way, you could have thrown her off guard a little and her immediate reaction was to put up her defenses. Maybe next time, you need to have a few more conversations with someone before asking them to hang out. Her reason for rejecting you also might have had nothing to do with you. Maybe she has a boyfriend and felt that her boyfriend wouldn't appreciate her hanging out with guys she met at work.

I know the loneliness is crushing, but please don't give up hope or give up trying. From the little I know of you, you seem to have amazing qualities and make a wonderful friend! I wish there was more I could say or do to make you feel better...