I hope her sister can convince her to see someone, if that's what she needs.

I am not sure why you wouldn't take what she says at face value? All of her actions and emotions sound sort of typical for someone ending a relationship. Sometimes apologies come too late. Sometimes people have unrealistic expectations of how much time another person should spend with them.

It can be extremely insulting to have someone attribute your feelings to an undiagnosed mental health issue. I would be very, very unhappy if my BF started trying to diagnose me when I had an issue with his behavior.

Instead of proceeding along this line of thought, I would go back to the original issue: was my time management reasonable? Was it reasonable for her to expect more support from me during her stressful December? What could I have done differently? Do I want to be in a relationship with someone who wants more time than I want to give and who stops talking to me things go haywire?