It could also be: Why don't you eat?
Instead of: Why do you not eat?
"Why do you not eat?" has one meaning: asking why the person isn't eating;
"Why don't you eat?" has two meanings: asking why the person isn't eating or offering that person to eat.
Anyhow I think both should be accepted.
And both are among acceptable translations
Why "why you don't eat" is not accepted? I was corrected to "Why do you not eat?", but that's the same?
In "why you don't eat" the word order sounds wrong. The verb should come second: "why don't you eat"
Should "Why won't you eat?" also be accepted here? It's also asking why the person is not eating, or is it too far off since it implies will and desire (will/won't)as opposed to pure function (did/don't)?