Actually, even though the story says it is for a limited time, it shouldn’t be too hard to find donors. (Though the whole health issue is a MAJOR consideration; many drugs and pathogens can be passed through to breast milk, such as garlic.)
It wasn’t too long ago that wealthy families hired full time ‘wet nurses’ to feed their infant children. (To help protect the mother’s figure.) These nurses would go from one family to another in their service for pay. As long as there is a demand, their bodies would keep producing the milk. Heck, if this catches on, we could have human dairy farms!