How much weight has she dropped? Have you seen her without clothing to even know what she looks like? Kids have great ways of fashionably hiding their emaciated bodies. I wonder just how "excellent" her health really is. Is this your opinion or is this the opinion of a medical doctor who is aware of her weight loss and has given her a comprehensive workup to check out her vitals?
I'm not surprised she denies anything's wrong. Believe me, you don't need another flare to tell you that something is wrong. Your daughter needs medical and psychological help, now! I wouldn't proceed with this in a desperate emotional manner. I would calmly, firmly tell her that you love her and care for her too much to let her health become compromised. Make an appointment with her primary care doctor and tell her what your concerns are, and research a therapist who has a good reputation for working with adolescent girls where eating disorders are suspected. I wouldn't be taking such a hard line if I hadn't seen these symptoms dozens of times before -- none of the cases I know of and/or have treated would have corrected themselves without some professional intervention. Good luck and keep me posted if you'd like.