The truth is, no one can say for sure. Peanut allergies are also on the rise in the little ones. Some kids do outgrow certain allergies, but this really does vary from individual to individual. For now, keep peanut products away from him and read labels and watch for warnings. There are labels warning of products that are not peanut products that say that they are made on the same equipment as where peanuts were processed. Be on the alert for this, depending on how severe his allergy is.
I'm sure your son's pediatrician or allergist must have also tested for all other nut allergies. Be on the look out even if he tested negative for the other nut allergies. People can have sensitivities that tested negative for allergies. So, watch for behavioral and mood changes, and watch for bowel habit changes. Food sensitivities can even cause headaches and sore throats--even if one tests negative for "true" allergies. Unusual hyperactivity or unusual lethargy can also be food sensitivities.
A simpler way to look at food sensitivities is the other layman's term is sometimes referred to as hidden food allergies. Such won't cause anaphylaxis or obvious skin rashes but can still make a person sick or feel sick.
You don't have to be hysterical or nervous, but just be aware. You don't have to drive the kid or yourself nuts, but just be aware.
It is hard to say, I have heard that folk's allergies can change every five years, but, with allergies that can cause fatal reactions such as peanuts, I would always be very careful.