J.L.
My son has also had eczema (mostly on his cheeks & chin) since he was 2 months old. When he was 10 months old we tested him for food allergies and found that he was allergic to many - cow's milk, soy, eggs, nuts, wheat, oat, citrus...
His allergist told me the food allergies are what cause my son to itch and scratch, and because of his eczema, the rash flares up and is at risk for becoming infected.
If the flare-ups continue, you may want to try elminating the foods that he might be allergic to. If you are breastfeeding, you might want to avoid eating those foods too (that's what I've been having to do...it's definitely tough, but makes a difference for my son).