Days. Appendicitis is an acute illness which leads to rupture if not treated within days of it's onset. Once in a blue moon, the body will seal off the rupture, leading to a prolonged low-level infection that can "simmer" for weeks; however, most people have so much pain prior to rupture that they seek out medical attention before this can occur.
Until fixed. Rarely it fixes itself! most will cause one to have an appendectomy. Some perforate and cause a lot of trouble. Their are some few reported with a chronic recurring pattern and later surgery.