The Web Browser element has 'Web Address' property that tied-up to the currently loaded web page. If participants navigate to another page that property is updated too. Thus, if you run the same web experiment second time, the Web Browser would start with the last visited page.
In order to start the the same page you can a) reload the experiment before restarting b) assign the initial page by code, for example in the 'Start' snippet:
WebAddress="http:\\www.google.com";