That's the dual edged sword of identity politics.  You can't play the woman card in an attempt to curry support from the Sisterhood without bleeding support from demographics that find that kind of identity politics off putting. Maybe her campaign did the math and thought it would be a net gain, but the more she played it and the harder she played it, the more she turned egalitarians, men, etc. off.  Did she gain enough to offset that loss by doing so?  

I'd argue that she already had the vote of the Sisterhood, simply by being the first female candidate for President. Visibly playing the woman card could only result in negatives for her campaign.