カスタム FacesServlet を使用すると、JSF フォームの送信時に認可リダイレクトが失敗するのはなぜですか?

<code class="java">import javax.servlet.Filter;
import javax.servlet.FilterChain;
import javax.servlet.ServletException;
import javax.servlet.ServletRequest;
import javax.servlet.ServletResponse;
import javax.servlet.http.HttpServletRequest;
import javax.servlet.http.HttpServletResponse;
import javax.servlet.http.HttpSession;

public class AuthorizationFilter implements Filter {

    private static final String AJAX_REDIRECT_XML = "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n" +
        "<partial-response><redirect url=\"%s\"></redirect></partial-response>";

    @Override
    public void doFilter(ServletRequest req, ServletResponse res, FilterChain chain) throws IOException, ServletException {
        HttpServletRequest request = (HttpServletRequest) req;
        HttpServletResponse response = (HttpServletResponse) res;
        HttpSession session = request.getSession(false);

        String loginURL = request.getContextPath() + "/login.xhtml";

        boolean loggedIn = (session != null) && (session.getAttribute("user") != null);
        boolean ajaxRequest = "partial/ajax".equals(request.getHeader("Faces-Request"));

        if (loggedIn || ajaxRequest) {
            chain.doFilter(request, response);
        } else if (ajaxRequest) {
            response.setContentType("text/xml");
            response.setCharacterEncoding("UTF-8");
            response.getWriter().printf(AJAX_REDIRECT_XML, loginURL);
        } else {
            response.sendRedirect(loginURL);
        }
    }
}</code>