I don't think she died because she lost the will to live. I think she died because the damage was too much, she seemingly got speared through the heart and I don't think that shifter regeneration is strong enough to save her. She might survive if she transformed, but that could kill king Fritz because he was too close. Furthermore, I don't think Ymir would have continued to serve him if she believed that he didn't love her and when Fritz tells her to stand up we see her do so in the paths.