After working as a Vet tech for many years, I have never seen this behavior in a dog. I have seen this happen in cats.
There is some underlying reason when your Chi will not eat. My suspicion is something like Addisons disease, Lyme, or other "hard to detect" condition. Has any Vet done a barrium series? That would rule out any digestive disorder. After that, I would consider testing for Addisons. It is a disease that presents iteslf in sometimes subtle ways. One being lack of appitite.
My Doc that I worked for always told me " a dog whill eat when it is hungry, if not, there is something wrong".
I wish you the best, you and your little one are in my prayers.