Food poisoning can certainly last a week. However, this is usually the point where you need to see a doctor. Most mild bouts last three days, maximum. This is accompanied, in most cases, by diarrhea and light vomiting. Dehydration follows, and so you must try diligently to stay hydrated. The first day or so will be futile, but it will work eventually. E. Coli is one of the few strains of food poisoning that is known to last up to a week without being serious enough to call a doctor or visit the hospital.
It should go without saying, however, that if you are worried or have a feeling that you need to see a doctor, it’s better to be safe than sorry. See the doctor if you’re worried.