She may have Addison's disease and really needs to be checked, call her endocrinologist, when you have one autoimmune problem you are at a increased risk of another, the adrenal gland makes cortisol amongst other hormones and this his a hormone that increases your blood sugar.
Be sure that this is not the problem as it is life threatening. If this is fine assessing her insulin regimen is critical, teenagers tend to stay up late, eat snacks late and may even bolus for the snacks, and go to bed, dropping their sugars.
Emphasize to her diabetes nurse that you would like to discuss this with her endocrinologist. Also the levemir in the evening may need reduced or if she is exercising even though her insulin is appropriate she may have late onset exercise related hypoglycemia and her muscles just become more efficient using glucose when she is not taking it in any longer (i.e. sleeping)
Get her checked and go over very very carefully with your teen her regimen and exact ratios and if she is indeed getting extra insulin that you did not know (2 shots of levemir by accident if she wasn't sure she got it, or extra novolog etc.)