-Have you tried the Haberman (SpecialNeeds) Feeder ? This is used for babies who have difficulty with bottles and nursing.
-How do you hold her when you breastfeed her or bottle feed her? When my mom breastfed O she would have him in almost a 90 degree sitting angle. It seemed to help him get more down, easier and it wouldn’t drip out of his mouth.
-My mom also would have O's twin sister, Y, nurse until she had a let-down and then Y would get taken off and O would get put on. This milk is called the "hind milk", which is higher in nutrients anyways, but it was also easier for him to nurse because the milk was right there.
There's also a couple things to consider if you have a baby who doesn't want to nurse because they get tired quickly
-How is the thyroid? A low thyroid (hypothyroidism) is very common in DS and it will cause sluggishness.
Does the baby have a heart condition at all? A heart condition will very often make a baby not want to eat much.
I know it’s very discouraging to see a baby who has little interest in nursing. I know it took a lot of work to get my brother going good on the breast. He had a bottle once, but we did not want him getting it much because we didn’t want him to get used to it. Once we did get him breastfeeding, he nursed until he was 2 years old.
Just keep trying and hopefully the baby will be able to do it well as you keep pushing her along!