Ah, family. We love them, but they exhaust and frustrate us.
You're right, her behavior is immature and hurtful; just realize that she does not, and never will, see it that way. It's not as if she knows that she's being self absorbed and alienating. She's convinced that her behavior is not only justified, but virtually inevitable.
I can't really tell you why you allow yourself to be hurt by this, except to say it's the same reason your mother allows herself to be hurt by the fact that people don't always agree with her. While you're thinking, "How can she do this to everyone around her?" she's thinking, "How can they do this to me?" I'm sure she allows the fact that you're an only child to ramp up the indignation on her part.
I view any kind of communication as an effort to help people understand others and their feelings, and I am forever butting heads with family members who feel that verbal communication is like a dance, and there are certain patterns everyone should follow. If you give a response that it outside the pattern, well, that's just rude. So, I'm frequently dealing with people who are hurt or angry because I said something they found unacceptable, like, "I like the blue one," or "My kids are in bed by then," or "I don't care for rare beef." I don't get it at all - this is no reason for anyone to be upset - but they cannot believe that I don't follow the "rules," and never disagree in the slightest. They are very much of the opinion that there is only ever 1 correct response to anything. Variation of any kind is not tolerated.
It also exhausts me that these same relatives find direct, clear communication of any kind to be just lower class and rude. They hint and hope people pick up on the hints. It's just exhausting. I'll take something literally - something like, "I don't make a big deal out of birthdays" - and they'll be furious and hurt because I didn't do the opposite of what they actually said. I am baffled by this. I am also baffled when I say something that I think is very clear, and they'll assume I mean the opposite. If I MEANT x, I would have SAID x, not y! Sigh.
Anyway, just be aware that you can do nothing about her behavior. When she gets in these moods, just behave as if it hadn't happened. If you normally call her every week, call her every week. If you normally e-mail every day, keep e-mailing. Don't try to talk her out of her funk, or apologize, or expect her to apologize. Just keep everything very normal - "Johnny did really well on his science test! We're so proud!" - and leave the ball in her court. If she chooses not to respond, OK. If she does respond, OK.
Hang in there! You are certainly not alone.