Loss of appetite is an indicator that your cat is ill, and something is wrong. If your cat is not eating at all for one to two days it could be an emergency, and you should get them to the vet as soon as possible. They may be a behavioral reason, such as stress, anxiety, or depression, perhaps caused by a change in surroundings. Try to encourage your cat to eat commercially canned food and try adding a little fish oil, chicken broth, tuna juice, or cooked egg.