Why can't I connect to a connect-served site over web sharing?

I'm using grunt, connect, and livereload to serve up a test page (it's a single flat HTML page) during development, and I want to test the site on my phone. Normally I do this using web sharing—by navigating to the site using my Mac's local URL (my-imac.local).

When I serve the page using Python's SimpleHTTPServer, this works fine. When I use grunt/connect, it's inaccessible there (though it's still accessible at localhost). How do I get connect configured to respond to these requests?

My gruntfile, for reference:

var path = require('path');
var lrSnippet = require('grunt-contrib-livereload/lib/utils').livereloadSnippet;

var folderMount = function folderMount(connect, point) {
  return connect.static(path.resolve(point));
};

module.exports = function(grunt) {
  function registerRobustTasks(name, tasks) {
    grunt.registerTask(name, function() {
      // so we don't have stupid issues with grunt crashing
      // every time a test fails...
      grunt.option('force', true);
      grunt.task.run(tasks);
    });
  }

  grunt.initConfig({
    pkg : grunt.file.readJSON('package.json'),
    livereload : {
      port : 48341
    },
    connect : {
      livereload : {
        options : {
          port : 48342,
          middleware : function(connect, options) {
            return [lrSnippet, folderMount(connect, '.')];
          }
        }
      }
    },
    regarde : {
      html : {
        files : ['*.html'],
        tasks : ['livereload']
      }
    }
  });

  grunt.loadNpmTasks('grunt-regarde');
  grunt.loadNpmTasks('grunt-contrib-livereload');
  grunt.loadNpmTasks('grunt-contrib-connect');

  registerRobustTasks('default', ['livereload-start', 'connect', 'regarde']);
};