As you have mentioned that with jQuery draggable everything works fine then I would suggest you to replace the jsPlumb draggable as:
droppedEleClone.draggable({
snap: '.dragme',
drag:function(e){
jsPlumb.repaint($(this));
}
});
And also while cloning make sure that you provide different ID's. DOM elements having same ID's doesn't yield proper result. Because of cloning the same object it's difficult to identify the right one and deleting it. Hence provide different ID's.