It's not simply because she's Fae, because so is the guy at the Inn in the present story and he doesn't speak that way, though it's entirely possible that he only doesn't because he's been with Kvothe for a while and has adapted human accents.

But I believe, if I remember, that Kvothe noted that Felurian spoke without any hard edges, an alien sort of inflection, a sound like birds, and the lack of capital letters is an attempt to convey that idea whenever she speaks. It's probably supposed to make us cringe, because Felurian is not human at all, and doesn't care to pretend to be. It's still a little weird, but it's a justifiable stylistic choice.