A cat that stops eating may be in pain, feel nauseous or be ill in, for example, the mouth, the gastrointestinal tract, the kidneys or other organs. Stress can also affect appetite, but it is important not to assume automatically that refusing food is just behavioural. Cats often show illness discreetly and may withdraw rather than show obvious symptoms.
Prolonged loss of appetite is particularly problematic in cats because it can contribute to hepatic lipidosis, a serious build-up of fat in the liver. Notice whether your cat is still drinking, whether it vomits, drools or seems to have difficulty chewing, and whether it has lost weight. The vet often first needs to find the cause of the loss of appetite and then assess the need for fluids, pain relief, treatment for nausea or nutritional support.
Contact a vet if your cat is not eating at all, or is eating much less than normal and the change persists. Seek help sooner if your cat is also lethargic, vomits, is in pain or already has a known illness.