I found this site which has a lot of research and treatment ideas by a doctor who treated children for eczema for a long time.
http://treatinginfanteczema.com/ click through to the chapters on the right side for details about digagnosis and treatment for many varieties of infant eczema.
In general eczema is treatable or even curable but the "answer" is probably different for everyone: ranging from diet issues to proper oils or even clothing issues.