It's a bit of an odd thing to say, but "never give up quality food" is grammatically correct. The definite article ("the") would not be used. Can you explain in a bit more detail the core idea you are trying to communicate? Another example of a similar grammatical construction could be: "never give up your dreams". Compare and contrast: "never give up on your aging father - he never gave up on you". Note the change in the verb from "give up" to "give up on".

This sentence should be written as: "Never give up quality food." However, a clearer and more natural way to express this would be to say something like, "Never give up quality when it comes to food." or "Never give up quality as far as food is concerned." Although this doesn't use "never give up," another good way to express the same thing is "Never compromise on quality when it comes to food."

Further to my previous answer, I am going to take a wild guess that what you actually mean is probably: "never give up on eating healthily" (see my comment a few moments ago explaining this)

It's hard to tell if it's quite right because there's no context -- can you provide some?