Is it possible to reference FacesContext from a TimerTask or ScheduledExecutorService on application startup?

Question

I am attempting to create functionality in a JSF1.2/ADF web app that will periodically & dynamically generate a sitemap for a website that will have hundreds of pages whose content will change daily. The catch is that I need to read some config from the application to use as the basis of the sitemap and to do so, I need FacesContext.

Here is what I have attempted to do: I created a class that implements a ServletContextListener and instantiates an application scoped bean. This bean does the heavy lifting to create sitemap.xml using FacesContext. I created a class that extends TimerTask that accesses the bean from application scope, calls the sitemap method and schedules future occurrences. When I run the application, the class that implements ServletContextListener fires and the bean appears to be created, but the class that extends TimerTask is never fired. Any help would be appreciated. If I can answer any questions or if I left anything out, please let me know.

Here are my code samples:

public class WebhomesApplicationContextListener implements ServletContextListener {
 private static final String attribute = "SiteMapGenerator";
  public void contextInitialized(ServletContextEvent event) {
  SiteMapGenerator myObject = new SiteMapGenerator();
  event.getServletContext().setAttribute(attribute, myObject);
 }
 public void contextDestroyed(ServletContextEvent event) {
  SiteMapGenerator myObject = (SiteMapGenerator) event.getServletContext().getAttribute(attribute);
  event.getServletContext().removeAttribute(attribute);
 }
}

public class SiteMapGenerator {
 public void generateSitemap() {
   // code to generate map...
 }
}

public class Scheduler extends TimerTask {
 public void run() {
  SiteMapGenerator sitemap = (SiteMapGenerator)FacesContext.getCurrentInstance().getExternalContext().getApplicationMap().get("SiteMapGenerator");
  sitemap.generateSitemap();
 }
}

class MainApplication {
 public static void main(String[] args) {
  Timer timer = new Timer();
  timer.schedule(
   new Scheduler(),
   1000 * 60);
 }
}