If you want to unstick element after the ajax response, just in the done function you can remove from this element class '.sticky' and add a stopper.
But after this, you need to scroll page to see effect

      $.ajax({
        url        : '/url',
        method     : 'POST',
        dataType   : 'json',
        contentType: 'application/json',
        data       : JSON.stringify(data)
      }).done(function(response){
        $("#sticky-element").sticky({
                stopper: 0
            });
        $('#sticky-element').removeClass();
      }

You can do it in two ways:

//It stops after a certain number of pixels 'stopper'
$("#header").sticky({ 
  zIndex:3, 
  stopper: 300 
});
//stopper is an element which stop the StickyContent. 
$(".sticky").sticky({ 
  topSpacing: 58, 
  zIndex:2, 
  stopper: "#footer" 
});