Why Is My Lactating Dog Losing So Much Hair?

Have your dog examined by a veterinarian to make sure there is no underlying medical cause for her hairloss.  Poor nutrition, ringworm, fleas, mites, infection, thyroid disease, or even barbering by the puppies can lead to hair loss.  Rarely increases in estrogen in dogs can lead to a dramatic loss of hair--the hairloss is usually on both sides and symmetrical.
It is important to rule out things that are contagious like ringworm, fleas and mites because these are things that can affect the puppies.  Poor nutrition also has secondary effects on the puppies.

Pregnancy and feeding puppies takes a lot out of a mother. Make sure to give her the best food possible. There are vitamin supplements out there too.
Peace