Don't play her game, dude. She's trying to control you, and make you feel like you've screwed up. You haven't. SHE is the one who wanted out, not you. Telling you that it's "your fault" that she is detaching herself from you because you're not at her beck and call is just manipulation.
Think about this logically. "You didn't respond to my text fast enough so I am going to divorce you." Does that sound AT ALL reasonable?