Here’s the short answer: It’s your story. You choose what—and what not—to revise. But there’s more to this issue. Let me fill in some of the details.
Usually a story will go through some sort of revision between acceptance and print and in many cases this close edit puts a polish on the work before it’s published. In fact, many publication contracts state that a story’s acceptance is contingent on revisions. Sometimes these revisions are light, other times they’re extensive. Usually an editor will mention more significant revisions upon acceptance. Or, if revisions are particularly lengthy or complex, he will not accept the work outright and instead encourage you to resubmit after you’ve revised. Always read contracts and other correspondence closely so you know what to expect.
The publication process can help you improve your work, so keep an open mind. If an editor is willing to engage in this revision process, he sees something promising. Do give serious and thoughtful consideration to the suggestions. This is a valuable opportunity to see your story through the eyes of someone with expertise and experience. Still, you may not agree that the suggestions are in the best interest of your story. Discuss your concerns with the editor. The conversation may allow for better understanding of the proposed revisions or open up new avenues in the story that intrigue you both.
In the end, not taking an editor’s advice may mean your story doesn’t get published at his journal. (This isn’t always true. It depends on how strongly the editor feels about the issue he’s asking you to revise.) Don’t fret. That just means your work isn’t a good fit with that particular journal after all. Keep submitting to find the right fit.
Your story—and your relationship with editors—will be strongest when you are open to the possibilities for improvement and you stay true to your intentions.