I would argue that gender identity CAN change and I'll give an example. I can count a couple of situations from my own personal experience. For instance, I'll be talking to people who don't know about Adyson. To them I've always been Adam. They will refer to me as "he" and they will think of me as male. Somedays, I'll have a distinct unconscious response to that. "No, I'm a SHE." Other days, if you refer to me as "she" I'll get the same response, "No, I am a HE". Just the other day, I was in a group of crossdressers and transsexuals. One of them referred to me as "he" and she covered her mouth in horror at her "mistake" . That day, I had a mixed identity, I was going for equal parts male and female, and was dressed as such. She made all these efforts to apologize to me, saying how she should have asked for my pronoun, despite my assurance that I didn't care, she was welcome to call me whichever pronoun she preferred. And at the time, I could care less what she called me.
For me, and individuals like me, the term genderfluid remains the same, but what that term means changes from day to day, hour to hour. My gender identity at least is very fluid, and changes all the time.
Anyway, I think that gender identity is incredibly difficult to pin down because its so intimately linked with our sense of self.
