Puppies should be checked every day not only for injury and signs of illness, but also to help them get used to being handled. One alarming sign of illness is bald patches or sudden loss of clumps of hair. As they get older, short-haired puppies tend to normally get thinner hair around the belly. Other than that, hair loss can note a health problem that needs immediate attention.
Puppies often get the fungal infection ringworm, because they lack immunity to it that adult dogs have. This starts out as small bald patches and eventually the puppy may go bald and scratch himself open.
"Dog Owner's Home Veterinary Handbook" notes that puppies can get thinning coats and bald patches because their bodies are not making enough growth hormone somatotropin.
Parasites can also cause the puppy to lose hair because puppies scratch and bite themselves. These parasites can be fleas or mites that cause demodectic mange.
"Dog Owner's Home Veterinary Handbook" notes that some breeds with black hair are prone to losing their black hair as puppies. Black hair follicle dysplasia is especially seen in Dobermans, Papillions and bearded collies, but can happen to mixed breeds.
All Over Baldness
"The Veterinarians' Guide to Your Dog's Symptoms" notes that beagles can be prone to alopecia universalis--being bald all over. This is a largely mysterious genetic condition.