Switching a legacy site to a responsive design takes careful consideration. After you decide responsive is indeed the way to go, over dynamic serving or separate web sites, then you need to do all your SEO checkpoints as if you are launching a brand new design.
The basic principles when launching a brand new design apply to launching a responsive design (assuming you change all your HTML structure to make it happen). You want to make sure of the following, if possible:
- Your URLs stay the same and if not, you have proper redirects in place
- Page titles remain the same
- Content on the page the same
- Navigation to the content stays pretty much the same
- Images and graphics on the page remain the same
- All the meta data remains the same
- All the basic SEO principles for a redesign are went over
You want to launch the new responsive design without changing too much, outside of the HTML and design. You want your content, images, URLs, navigation and so forth to all be the same as it was.
If you do all of that, you really should not see a change in rankings or indexation by the search engines. But like with any major design revamp, you need to make sure you test, test and test to make sure you didn't forget anything. And after you launch, watch those 404s, errors and analytics for things you may have missed - because if catch them fast and fix them fast, all should be good with your rankings.
Forum discussion at WebmasterWorld.