WCF is hosted by IIS, and thus subject to its lifetime rules. A service class, by itself, will probably be created and destroyed as necessary within the app; the class will be constructed upon receipt of a request, the method called, and the result returned, after which the object will leave scope and be disposed/finalized.
However, the project containing your service looks like an ordinary ActiveServer.NET web app to IIS (check out the Global.asax file that should be in it; it contains a class of type HttpApplication, and represents the entry point for the app that IIS can use to control it), and IIS will maintain a "pool" of these applications to handle requests from multiple clients. As long as requests keep coming in, and IIS doesn't decide an app has gotten "stale" and refreshes it or the entire pool, the application will continue to run. So, any static classes you declare, for instance your singleton IoC container, or anything you add to a derived HttpApplication class that you use as your child type, will remain in memory until the app is recycled.