According to the ASPCA, the most common reason for puppies to lose their appetite and vomit profusely is due to eating something they should not have. However, there are a variety of other medical issues which may cause similar digestive problems. Regardless, the best course of action is to take the dog to a veterinarian as soon as possible.
Due to their age, puppies are often susceptible to a variety of ailments which adult dogs can easily fight off. It is also not uncommon for puppies to vomit as a result of consuming their food too quickly, according to About.com Puppies.
There are also a number of more serious maladies which can cause excessive vomiting, some of which are life-threatening. If the animal in question has recently been adopted it can be a good idea to make certain that their immunizations are up to date. Certain pathogens and viruses are intentionally immunized against simply because of how common they are. According to Pet MD, the Parvo virus is one such example, though this is normally accompanied by frequent and uncontrollable loose stool, usually watery in consistency.
The ASPCA cites several, much more serious and less preventable, systemic issues which can include vomiting as a symptom. If a puppy vomits more than once, it is best to err on the side of caution and simply take it in to see a veterinarian.