For years, China’s net nannies turned the other cheek to a loophole in their vast online censorship apparatus. Anyone who wanted access to blocked overseas websites such as Twitter, Facebook, and more recently, the New York Times, need only download foreign software called a virtual private network (VPN) to circumvent the Great Firewall. But in recent weeks, even these tools have begun to falter, frustrating tech-savvy Chinese and foreign businesspeople who now struggle to access Internet sites as innocuous as gmail.com and imdb.com.