Updated source code for example on StackOverflow and the Phaser forum

main.js

var game = new Phaser.Game(800, 600, Phaser.CANVAS, "game", {preload: preload, create: create, update: update});

var dude;
var block;
var spacebar;
var gameOverText;

var gameOverCounter = 0;
var gameOverBool    = false;

var downCounter = 0;

function preload () {
  game.load.image("block", "assets/block.png");
  game.load.image("dude", "assets/phaser-dude.png");
}

function create () {
  dude  = game.add.sprite(373, 760, "dude");
  block = game.add.sprite(0, 505, "block");
  
  game.physics.arcade.enable(dude);
  game.physics.arcade.enable(block);
  
  dude.body.collideWorldBounds  = true;
  dude.body.gravity.y           = 200;
  
  block.body.collideWorldBounds = true;
  block.body.immovable          = true;
  
  block.body.velocity.x         = 100;
  block.body.bounce.x           = 1;
  
  var jumpOrTryAgain = function () {
    if (gameOverBool === false) {
      dude.body.velocity.y = -250;
      
      console.log("down");
    } else {
      dude.destroy();
      block.destroy();
      gameOverText.destroy();
      
      gameOverBool    = false;
      gameOverCounter = 0;
      
      create();
    }
  };
  
  if (downCounter === 0) {
    spacebar = game.input.keyboard.addKey(Phaser.Keyboard.SPACEBAR);
    game.input.onDown.add(jumpOrTryAgain);
    spacebar.onDown.add(jumpOrTryAgain);
    downCounter += 1;
  }
}

function update () {
  
  function gameOver () {
    if (gameOverCounter === 0) {
      gameOverBool = true;
      dude.body.velocity.y  = 0;
      dude.body.velocity.x  = 0;
      block.body.velocity.x = 0;
      gameOverText = game.add.text(300, 200, "Game Over!", {fontSize: "16px", fill: "white"});
      gameOverCounter += 1;
    }
  }
  
  game.physics.arcade.collide(dude, block, gameOver);
}