It does not mean that viral fevers do not last more than 3-5 days. But often by the time you decide to watch fever at home and visit a doctor for a fever of three days... its almost always settling if the fever were of viral types. If its not... may be its not a viral fever.
A viral fever may cause other symptoms or weakness that may necessitate a doctor visit even though fever is settled. In bacterial fevers often the fever doesnot settle unless specific therapy initiated.
All fevers do cause reduced intake of solids and eventually making one feel weak.. thirsty and lethargic. Its important to maintain good water intake during all patterns of illnesses observed at home. I recommend half a cup of water as medicine every hour at least 8-10 times a day for say a five year kid to maintain good hydration and urine. "Do offer other diet and feeds but dont force solids" out of child's will if he can't swallow say due to throat infection or cant digest.. say due to gut infection. Its not exactly a loss of appetite but inability to accept feeds in gut. Often such reduced intake persists for a week after any disease and donot need appetite drugs but good control of disease and enough water. In any disease.. care to be taken to have enough water or liquid intake ao that child will pass urine at leat two times in 12 hours (its never a medical emergency if a child doesnt pass stools for 2 days unless child has very bad vomit/colicky pain in abdomen)... if not... your doctor will be worried that the kid is likely to require hospital admission mainly to ensure superwised intake or iv fluids and also simultaneous disease control.