Problems Feeding

Amanda • First time mom. Married to an amazing man. 3 meowing furbabies. Roadie. Entrepreneur. Lexus IS350 F Sport enthusiast.
I have a late term preemie (born on March 25th at 35 weeks) and I am struggling to feed him. He falls asleep while nursing or bottle feeding (breast milk) and it seems like every feeding is a battle. 
Anyone else in the same boat? Anyone dealt with it successfully? Any tips or light at the end of the tunnel? 
Thank you! :)