In my experience, eye contact is usually something a girl will give you if she finds you somehow appealing to her eye. Girls will rarely look a guy in the eye who they don't find attractive, especially if they don't know them. There is an exception sometimes if the girl knows the guy well enough, because after they know them, they will feel better looking them in the eye.
I have not had problem with eye contact from women, and they are normally trying to look me in the eye more than I am trying to look them in the eye sometimes. I find that I will try to look a girl in the eyes more when she's hot than if she's not. However, when I started to do it more consciously, I practiced by looking every girl in the eye not matter how attracted I was.
I'd hate to say it, but maybe you might not be the world's most attractive guy, which only means you'll have to just work a little harder to grab the attention of the girls you want. Do this by making sure you have some charisma and a good sense of humor, which is easier said than done.