data: function ()  {
  return {
     questions: [],
     sendButtonDisable : false
  }
},

methods: { 
  postQuestionsContent : function() {
    // This works here.
    this.sendButtonDisable = true;

    // The view model.
    var vm = this;

    setTimeout(function() {
      // This does not work, you need the outside context view model.
      //this.sendButtonDisable = true;

      // This works, since wm refers to your view model.
      vm.sendButtonDisable = true;
    }, 1000); 
  }
}