Should I just move on from my demanding girlfriend?

My girlfriend and I have broken up and gotten back together numerous times in the past two years. We recently just broke up again last night on New Year's Eve. When we break up, the very next day, she calls me and acts as if nothing has happened. She acts like everything is alright. This has been going on for two years. I do love her and care about her and her children a lot, but she seems really demanding as far as what she deserves from a man. She is always telling me that she deserves this and that from a man. It makes me feel like crap because I cannot give her everything that she wants. She told me one time that she wants a man who is going to be afraid to lose her. Is that a normal thing that women want, or should I just move on already? I am in my 30s and she is in her 40s.