It sounds like your girlfriend is feeling rejected by you. I have the sense that she wasn't responded to properly as a little girl.
If I am right, her mother and/or father pushed her aside when she needed them. This early experience scarred her and I sense that each time you are too busy for her the old wound with her parents is ripped open and she feels deep pain.
What you want to do is this: The next time she calls, try to be responsive to her. If you can postpone the activity you're engaged in and put her first, I think that you will be amazed at what a healing experience this is for her.
Your putting her first will be like a healing balm for her soul and the hurt little girl inside her will begin to feel as though her feelings are indeed important to someone. A few of these experiences will be transformative for her.
After her needs have been responded to for a period of time, she will feel less needy and it will be easier for her to accept when you are involved. If and when you find it impossible to be responsive, make sure that you embrace her with your words before saying no to her request.
To do this, say, 'Honey, I'd love to listen to you now. You know how important you are to me, but. . . (say what you must do that you can't postpone). Then make a raindate to talk to her.