Why is my son still very sick after a week of having hand foot mouth virus?

Followup is advised. I would recommend a followup with your pediatrician. In most cases, a week into hand-foot-and mouth disease, most children are starting to feel better. If he is not improving, it is worthwhile to make sure his doctor checks him to be sure he does not have a secondary bacterial infection (such as an ear infection that may warrant antibiotics).
Hand Foot.... And mouth virus caused mostly by coxsackie virus, usually lasts anywhere from 7-10 days but can linger for up to 2-3 weeks. If he is still not better after 10-14 days, a return trip to the pediatrician is needed, or possibly a referral to a pediatric infectious disease specialist.