Draggable should stop automatically when you release your mouse.
HTML
<body>
<div id="draggable" class="ui-widget-content">
<p>Drag me around</p>
<p id="position"></p>
<p id="event"></p>
</div>
</body>
JS
$( function() {
$( "#draggable" ).draggable({
scroll: false,
drag: function( event, ui ) {
$('#position').html(
'Left : ' + ui.position.left + '<br/>' +
'Top : ' + ui.position.top
);
},
start: function( event, ui ) {
$('#event').html("Dragging");
},
stop: function( event, ui ) {
$('#event').html("Stopped");
}
});
} );
Try the sample above. The dragstop event is automatically called every time you release your mouse from dragging. Try apply this in your code to further investigate why the dragstop is not being called in your case.
http://codepen.io/jyloo/pen/mrZmjO