A função $.detach() remove os elementos do dom preservando todos os dados e eventos.

$.detach()

//.detach() removes the list from the DOM, then it can be modified and reinserted into the status element.
//.detach() removes an element from the DOM, preserving all data and events.
This is useful to minimize DOM insertions with multiple html elements.
$('.update-available-flights').on('click', function() {
    $.getJSON('/flights/late', function(result) {
        var flightElements = $.map(result, function(flightItem, index){
        var flightEl = $('<li>'+flightItem.flightNumber+'-'+flightItem.time+'</li>');
        return flightEl;
    });
    $('.flight-times').detach()
                      .html(flightElements)
                      .appendTo('.flights')
    });
});