Please don't hate me for saying this! But, I think it's because she's kind of boring. I mean, she's a pretty young white girl with a pop sounding voice, of which there are many. Combine that with not having an incredibly tragic backstory or funky glasses and you've got a montaged singer. If you think about it, nearly everyone else the coaches have kept around has something really unique about them, whether it is the way they look, their backstory, or their genre of music. This has always been true on the show to some extent, but I feel like in past seasons they were more open to choosing your run-of-the-mill pop singers. Last year and this year in particular they seem to be bypassing those folks in favor of building "unique" and "eclectic" teams. Even in the blind auditions where they can't see the singers, someone unique-looking like Michelle Chamuel gets chosen because of her song choice.
So basically, if you're not able to truly differentiate yourself in some way, you won't get through. While Amy may be a good singer, she probably just doesn't stand out enough as a personality to win the whole thing. You can argue that that's wrong since this show is called "The Voice," but it seems like that's just the way it is.
