That's an odd case for us, as we're focused on using it for testing.
Some possibly useful information for your case:
* Capybara::WebKit::Connection is the class responsible for starting and stopping the server.
* Connection has a private method called "kill_process" that will shut down the current server.
* You could potentially change Connection to have a public "restart" method to cycle the process. Assuming it didn't introduce a significant maintenance burden, we'd take a tested, well-factored patch to add the method.
If you don't feel like submitting a patch and just wand a workaround, you can try calling the private "kill_process" method and starting a new capybara session.
-Joe