Would it be helpful to start integrating breaks in the iPad use to engage in other activities with your patient instead of using it until the batteries go dead? Maybe consider allowing the iPad to be used during feedings (if they are bolus) or other "quiet times". If all of a sudden you stop using the iPad, I'm guessing the patient won't be very happy! Maybe it would also be helpful to shift your approach from "distracting" your patient to "engaging" your patient. If she is able to focus on the iPad for a length of time, that's great because it means there could be other activities she will be able to engage in.
Starting to create a routine with this patient and addressing the environment can be very useful having a more positive-interactive relationship with this patient. If there is a routine during other day shifts, this might be a good place to start. If the child has PT/OT/ST then maybe ask them for ideas for similar activities you could do with your patient. They may also have ideas as to what calms this particular patient when she starts getting wound up. The other children in the residence may be a good source of info for identifying activities your patient enjoys. Keep in mind kids with autism that I've worked may have a short attention span, especially for a new activity. It also may take several attempts for her to be able to enjoy a new activity. It can also be a trick to figure out what she needs/wants and learning to address those needs/wants early.
Best of luck with discovering some strategies that work for your patient!!