The phrase "to refuse the breast" means that a baby or young child does not want to drink milk from their mother's breast. They may show signs of not being interested or pushing away when offered the breast. Full definition
If you find you aren't nursing as often as you need to, pump when baby refuses the breast in order to keep up stimulation and, ultimately, your breastmilk supply. (lansinoh.com)
About a week later she just started refusing the breast on a little strike. (justbreastfeeding.com)
He will drink juice from it, but refusing breast milk or formula in the bottle. (babycenter.com)