I have had mother dogs and the behavior comes from wolves and wild dogs. In the wild the mother dogs hunt and then come back and regurgitate the food for the pups to supplement the milk.
A balanced female actually starts weaning the pups completely about 9 weeks. If she is a hunting dog she may start taking them out stalking or chasing in the yard.
I've never had a problem with the mother continuing to regurgitate. Once the mother starts weaning the remaining pups on her own, they should all be removed to a separate area and only allowed with the mother at night, if at all. If you keep one and return it, after the mother's milk has completely dried, to run in with the mother dog, you would hope she would no longer show any urge to regurgitate for the pup. However, there are no hard and fast rules, like with our mare whose 3 year old was turned in the same field after she had raised another foal in between, and she had no milk or foal on her side but let the 3 year old nurse. Go figure.
I'm hoping there is a breeder lurking on this site who can give us more insight.
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