If you are concerned, do a simple blood test to make sure that the red blood cells and white blood cells are reasonably normal or normal enough to accept the "viral" diagnosis. Since it's been going on for a while, I'm sure it's just some peculiarity that your son's body does when he's mildly ill - but why not allay your fears with a simple blood test?
Since you have mentioned this to your doctor on several occasions, I would consider finding a new pediatrician. It bothers me that he has dismissed your concerns without minimal testing. My pediatrician has never dismissed any of my concerns. That's not to say that he hasn't calmed my fears on many occasions. He has been our pediatrician for 14 years and, even though, we now live one hour away from his office, I still would not change doctors because of the concerned, professional care that my family receives from him and his staff.
Best of luck to you!