Unworthy? No, I wouldn't use that word. Out of my league maybe, but that's just rational assessment - a multigadzillonare rocket scientist who models on the side is probably not going to be interested in little old me who is still going to college at 26 and despite going to the gym frequently, can't seem to shake the love handles.
As far as girls too good to give up on, yes and no. The girl you think is too good to give up on, you're probably overdoing it with, so if you give up, in my experience, the interpersonal aspect you two have actually improves, which may or may not lead to a relationship. It's almost a catch 22 so I try to avoid thinking like that.
Perhaps as a teenager I would consider myself unworthy some girls. But that's simply a result of low self-esteem. Nowadays I consider everyone to be equal humans and I don't place certain people on pedestals. What would keep me from giving up today would be if I realize that we have too little compatibility in terms of personality and lifestyle.
I did last year, but she was actually after me. I was still recovering from a rather nasty situation I'd been in and because of what I'd been through, I couldn't understand why a girl like her would have wanted me :-/