Child Theme is highly recommended if you’re doing ANY changes to your Theme design, including the basic style.css changes. Child Theme will look 100% the same as Responsive Theme and give you the ability to modify everything, while protecting and safe-keeping your changes from the future updates.
A WordPress Child Theme is a Theme that inherits the functionality of Responsive Theme also know as the parent Theme, and allows you to modify, or add to, the functionality of parent theme.
To give you a head start we’ve created fully working Responsive Child Theme example for you. Please feel free to download and modify any way you like.
Child Theme needs to be either uploaded via FTP or simply over WordPress dashboard, when the Theme is on your site click activate and that’s it. When Responsive Theme is upgraded your Child Theme and all of your modifications will be safe and remain unchanged.
Just in case that you need also see Child Themes Documentation from WordPress Codex.