Page changes made via Firebug or via Javascript do not persist from one page load to another. Each time a page is loaded, the original HTML, CSS and JavaScript is parsed and loaded (from cache or from the server). Any prior changes will not be there.
The only way for a dynamic page change to be still present after a refresh is for you to save the changed state to a persistent location and then rebuilt the appropriate page content from that state each time the page is loaded.
But, if you make a change to the page and store some state in a cookie, in local storage or on your server, then you can have JavaScript that runs each time the page loads that gets that state from wherever you stored it and then applies the appropriate change to the page. If you're saving the state on the server (on behalf of this particular user), then you could even have the serve modify the page contents before it is served to the browser.