Hello Jake. I don't have a diabetic child, but I was one, diagnosed at 16 back in the dark ages of diabetes care ('68). I wonder if your daughter might be growing into a woman. Because the hormone swings that come with this new territory can wreak havoc on basal rates. Is she menstruating yet or showing signs she will begin soon?
When I went on the pump I learned why MDI had never worked well for me - Because my basal rate varied so much in a 24 hour period as well as over the 4 week menstrual cycle.
My evening rate was highish -.550/hr. - through the supper hours; then dropping to .2 or .15 from 9pm-midnight; down further to .1 or even less, 12am-3am; then up to .4 from 3am-5:30am; .7, 5:30am-8am; and 1.0 8am-11-am; finally .4 from 11am-4:30pm.
In 24 hours my basal ranged ten fold, .1 to 1.0!
The other problem with some of us is that our basal rate as a whole rises or drops by x% during different parts of our cycle. After ovulation it climbs for 2 weeks then a steep drop as the period starts (down as much as 40% in my case) then slightly up and stable for two weeks prior to ovulation again.
This can be handled by creating multiple basal patterns for each part of the cycle. When 2 or 3 bad tests high or low happen she just switches to the next program.
I know both the beginning and end of menstruation is challenging for T1's as whatever pattern we are used to changes dramatically and often for awhile. If that IS what is happening to your daughter it is frustrating, exhausting and worrisome... but most likely normal. Just keep trying. It will settle out eventually!
Best luck!
-Linda