What could cause three of six puppies to die out of a litter?

Tons of things could have caused the puppies to die, and its actually quite commen for the entire litter not to survive. It could have been the weather, trauma during the birth, the mother being too rough, the mother not letting them feed (sometimes animals wont feed the sickly ones or the runts of the litters since in the wild they wouldnt survive and its taking milk away from the healthy ones that would survive), or it could be a problem the were born with also.

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It could have been a lot of things. We had all the males in the litter die a few years ago. So that was obviously something genetic.