If a puppy receives a vaccination for rabies before the maternal rabies antibodies are gone, the vaccination is blocked, and no immunity develops.
The same is true for the other components of the vaccines—the temporary immunity received from the mother can interfere with all the vaccinations.
If the dog has a disease that suppresses the immune system or takes immuno-suppressive medication, it will not respond.
If the dog has a fever, the immune system will be so occupied with the fever that it will respond poorly to the vaccine.
Ideally, vaccinations should be given shortly after the maternal antibodies are gone but before the puppy is exposed to infectious organisms.
If the maternal antibodies have waned after one vaccination and the puppy is exposed to the disease-causing virus or bacterium before the next vaccination occurs, the puppy will likely develop the disease.
The opposite problem can occur if a vaccine is mishandled.
The vaccine can become virulent or cause the infection it is intended to prevent.