Rejecting breast

My daughter is around 6 weeks old and i am breastfeeding her about 10 times a day. Since last week or so she started this strange pattern where she would feed for about 30-40 mins , get drowsy almost fall asleep but then suddenly wake up and get all fussy. At that point she just does not want the breast at all and is only calmed down if I give her a bottle of expressed milk. Has anyone experienced this? Any tips/suggestions would help as I am really frustrated having to double feed and feeling like she did not get anything out of the breastfeed :(