My daughter has eczema and I eliminated all allergens I could think of and nothing seemed to help and we finally figured out she has lots of environmental allergies, mold, grasses, trees. We added a couple of HEPA filters to her sleeping room and main play area and that has helped, as well as washing her after being outside playing. We are also doing sublingual immunotherapy and I really think it is working.
Good luck. Eczema is so tricky.