It's possible she couldn't. Some vegans (yes, not all or even most, before vegans jump down my throat) aren't very healthy and she might have been nutrient deficient to the extent that she wasn't producing milk. She may have not produced enough milk unrelated to her diet, as some women just can't breastfeed. Or she might not have thought it ethical. There's debate in the vegan community as to whether human breast milk is vegan or not. Most vegans will say it's fine, that there's no issue with breastfeeding, but some more extreme types disagree. Or she might just have not wanted to.
Poor baby. Why on earth did they think potato could sustain a baby, who needs a high fat high protein diet?