Just wanted to make sure that the doctors checked/looked for Celiac disease.
She could also be severely allergic or even intolerant to certain foods and is getting sick because she's getting those particular foods through your breastmilk (meaning you're eating the foods that her body can't handle).
You state she has no problem tolerating breastmilk, it's when the food gets into the intestines that she starts having issues. That points to the fact that it's food related. Unfortuantly, I don't have a lot of faith in conventional medicine finding problems/causes of food issues. I had to see a naturopathic doctor/alternative medicine when I was 40 years old, which was when I finally learned I had casein allergy (to cow's milk and cow products) and was severely intolerant of gluten and soy. No wonder I was so sick all my life and had asthma!!
Now that I don't eat cow products, my asthma is COMPLETELY gone! And now that I don't eat soy and gluten, all my other mysterious ailments have also gone away. However, unless you get a doctor who will do an Elisa/RAST(?) test, you won't probably find out much. Conventional doctors/medical community don't believe that food can cause issues with the body, so they poo-pooh anything having to do with a link with food and issues/problems.
I had to go the alternative medicine route to find out my issues, which also included heavy metal toxicity, severe malabsorption, severe deficiencies in vitamins, minerals, enzymes, amino acids, etc. I found out spring 2010 I had a virus that was hiding in my body, and fall 2010 I discovered I have moderate adrenal fatigue. Not finding food issues will lead to a lifetime of health problems and issues. Mine lead me to taking 12 different pharmaceutical drugs. I'm now off all pharma drugs except for one for high blood pressure, and I'm working on getting off that one too.
By the way, babies can be born with heavy metal toxicity. I had my daughter tested when she was 8 years old, and she was more toxic/poisoned than me, who has 32 years on her for living. Conventional medicine doesn't believe in this; I have no idea if they would even test for this. A naturopathic doctor will. The test is simple and very inexpensive.
I think it's absolutely awful that they won't allow her to eat. Do they at least have an IV line in so that she doesn't become dehydrated?
You have to be an advocate for your daughter. I'm not sure how much you can push for certain tests with the allopathic community, since they only have certain tests/labs they can do, but if the doctors are truly at a loss as to what is making your baby so sick, I would suggest the Elisa/RAST(?) test and see if they would be amendable to doing it, even if they, gasp!, have to have an Integrative Medicine doctor perform it/send it out to the lab. Most conventional doctors/hospitals do believe in Integrative Medicine. I don't know if Children's Hospital does, but I would definitely look into food allergy/intolerances if she were my daughter.
My prayers are with you and your daughter. I hope they find the reason soon.