I've had a fishing line grid up for over a year now and no hawks have tried to enter the runs. They sometimes sit in a tree and look and often cruise over. I did lose a baby a few days ago when it went through the fence and outside of the run. The same hawk came back the next day and was waiting for another little one to leave the covered area, but didn't try and go into the run.
I have the lines spaced about a foot apart, with heavy fishing line. The only problem I have is the squirrels run across the top of the fence and the lines and break the line from time to time. It doesn't stop two determined girls from getting out of the run, but I've never been able to keep those two inside a run when they wanted out.
So far it's held up much longer than the plastic netting I've used.