Perhaps I have not made myself clear, by my saying I'm losing patience I more mean I am frustrated. I have been very patient with her. Spending hours with her so she can enjoy being outside. Maybe don't spend hours with her and let her work it out. She is not picked on by the other hens in fact she herself tends to pick on the younger birds. My lowest on the pecking-order hen wasn't picked on by the hens her age, but she did go after the younger ones. I knew she was lowest on the pecking ordeer because the other hens would push her away from the feeder and not let her roost in the prime spots. I think a lot of her problem is she has become too reliant on me. When I go to the coop and she sees me she starts squawking loudly until I go to her. Then stop going to her and let her squawk. She likes to ride on my arm outside or be put on something up off the ground. If I put her on the ground she runs around dashing here and there for a few seconds then runs back to me and looks up wanting me to pick her up. If you stop picking her up, eventually she'll stop expecting it. She does this even if the roosters are not nearby. It takes awhile each day just to get her comfortable enough to stay on the ground near my chair for a bit.
Another odd thing I have noticed when I go to shut the coop at night is she apparently doesn't mind sleeping next to a rooster on the roost. That doesn't bother her at all. More often than not she is beside one or the other of my roosters and looks comfortable. So perhaps now you can see why I'm pulling my hair out. She is a quirky little chicken but I like her and want her to be happy and be comfortable on the ground.
