I insert element from the php file as a result of successful ajax call. But for some reason that and everything in it is missing when I look at my source code of the page. It
You're most likely binding the click event handlers to your delete divs on document ready. When you add new divs, the click event handlers are not automatically bound to the new elements.
So, after updating your data, bind the event handlers again, and you will be good to go.