I have been working on being more honest in relationships, and more willing to address issues rather than stay quiet and feel resentful. I have always been afraid of hurting people's feelings, so I tend to stay quiet even if I'm upset.
I sent my friend what I thought was a nice-as-possible e-mail saying that I understand she's busy, but I am sad that she wasn't in touch with me when she knew I was going through difficult times this summer. This is the first time I've ever addressed an issue like this with her.
She blew up and now says I owe her an apology for confronting her when she is so busy and overwhelmed. I am at a loss - other than not bringing it up at all (and getting more and more resentful), I don't know what I could have done.
This could end a 15-year friendship, because I am not willing to apologize for raising what I think is a reasonable concern. I'm now even more hurt at her refusal to recognize my feelings as valid. Because I have always avoided things like this in the past, I don't know how to handle this.
Answer: Actually, you do know what you could have done: You could have remained Old You, and been the friend who never says anything. After all, that's the person your friend plucked from the crowd 15 years ago.
So it's important to realize that when you decided that your character had room for improvement (a difficult and laudable step), you took the chance that you were changing traits others liked. Some people seek out convenient or compatible flaws in their companions, or simply like someone as-is, and regard metamorphosis with a sense of loss.
It's worth trying to find out whether your friend can come around to considering your needs along with her own. Be kind and firm in maintaining that you didn't ask anything from her that you didn't have a right to request; remind her, too, how difficult it is for you to speak up.
At the same time, be open to the possibility that your "nice-as-possible e-mail" was a clunker. Misreading tone is a hazard with all communication, but it's a particular danger with writing. (Another thing you could have done differently is called, or confronted her in person.)
Here's the variable on which I believe your friendship hinges: If you spent 15 years caring about each other, then there's a good chance she will come around. If she spent 15 years taking advantage of your compliant nature, then the new you might not want this friend anymore.