Whenever the map triggers the idle event (this occurs when the map becomes idle after panning or zooming, you can refer to the documentation here), it's important to duplicate the markers. Prior to adding new markers on the map, it is recommended to CLEAR those existing markers by iterating through the markers array and setting the map value to NULL.

var i = 0;
var total = markers.length;
for (; i<total; i++) {
 markers[i].setMap(null);
}

Following this step, a complete REBUILD of everything should be performed. The Clusterer functionality changes at this point. Therefore, encapsulate the call to the clusterer in a function and execute it each time the markers array undergoes modifications. This approach should effectively handle the task!

I hope this explanation proves helpful!

EDIT: Provided below is a revised version of the code. Although not optimized, take some time to analyze it and understand the modifications made. Comments have been included to aid comprehension. PLEASE NOTE THAT THIS CODE HAS NOT BEEN TESTED.

Here is the revision:

// Presumably, this segment exists within your code
var map;

/**
 * Initialization function
 * @param  {float} lat Latitude
 * @param  {float} lng Longitude
 */
function initialize(lat, lng) {
    window.lat = lat;
    window.lng =lng;
    var myLatlng = new google.maps.LatLng(lat,lng);
    var mapOptions = {
      mapTypeControl: false,
      center: myLatlng,
      zoom: 13,
      maxZoom:18,
      zoomControl: true,
      mapTypeControl: true
    };

    map = new google.maps.Map(document.getElementById('map-full'), mapOptions);
    google.maps.event.addListener(map, 'idle', function() {
        $mapBounds = map.getBounds();
        getJSONData($mapBounds);
    });
}

google.maps.event.addDomListener(window, 'load', initialize(<?=$location;?>));

/**
 * Retrieves JSON data for the map
 * @param  {array} map_bounds Boundaries of the Google map post-idle
 */
function getJSONData(map_bounds){
    var bounds  = {
        'swlat':map_bounds.getSouthWest().lat(),
        'swlng':map_bounds.getSouthWest().lng(),
        'nelat':map_bounds.getNorthEast().lat(),
        'nelng':map_bounds.getNorthEast().lng()
    };

    data = {
        'bounds': bounds,
    }

    $.ajax({
        type: "POST",
        dataType: 'json',
        url: "<?=$data_URL;?>",
        data: data,
        success: function (json) {
            populateMap(json, bounds);
        }
    });
}

// Tracking markers and clusterer
var markers;
var markerCluster;

/**
 * Generates the map with the provided data
 * @param  {json} data    Map data
 * @param  {array} bounds Map boundaries
 */
function populateMap(data, bounds){

    // Assuming the capability to clear markers and clusterer
    // If present at this stage
    if (markers.length) {
        var i = 0;
        var total = markers.length;
        for (; i<total; i++) {
            // Eliminate click listeners
            google.maps.event.clearListeners(markers[i], 'click');
            markers[i].setMap(null);
        }
    }

    // Restart the process
    markers = [];

    if (markerCluster) {
        // Remove click listeners
        google.maps.event.clearListeners(markerCluster, 'clusterclick');
        markerCluster.setMap(null);
    }

    // Restart the process
    markerCluster = null;

    // UNTESTED PORTION BEGINS FROM HERE
    var infowindow = new google.maps.InfoWindow();

    leftList(data); // appends properties to the left list
    for (var i = 0; i < data.length; i++) {


        var latLng = new google.maps.LatLng(data[i].lat, data[i].lng);  
        // place the marker
        var marker = new MarkerWithLabel({
            position: latLng,
            map: map,
            labelContent: data[i].price,
            labelAnchor: new google.maps.Point(27, 35),
            title: data[i].title,
            labelClass: "map-markers",
            infoData: data[i],
            zIndex: i

        });

        google.maps.event.addListener(map, 'dragstart', function() {
            infowindow.close();
        });

        google.maps.event.addListener(marker, 'click', function() {
            infowindow.close();
            var info_content = makeMarkerInfo(this.infoData, this.index);
            infowindow.setContent(info_content);
            infowindow.open(map,this);

        });

        markers.push(marker);

    }

    ///// ADD CLUSTERS
    var clusterOptions = {
        zoomOnClick: false
    }

    markerCluster = new MarkerClusterer(map, markers, clusterOptions);

    // Zoom in or display infowindow upon clicking Cluster
    google.maps.event.addListener(markerCluster, 'clusterclick', function(cluster) {
        if (map.getZoom() < map.maxZoom ){
            map.setCenter(cluster.center_);
            map.setZoom(map.getZoom() + 4);
        } else {

            var content = '';
            // Converting lat/long from cluster object to a useful MVCObject
            var info = new google.maps.MVCObject;
            info.set('position', cluster.center_);
            // Obtain markers
            var marks_in_cluster = cluster.getMarkers();

            console.log(marks_in_cluster);

            for (var z = 0; z < marks_in_cluster.length; z++) {
                content = makeClusterInfo(marks_in_cluster,z) ;
            }
            infowindow.close();
            infowindow.setContent(content);
            infowindow.open(map, info);
            google.maps.event.addListener(map, 'zoom_changed', function() {
                infowindow.close()
            });
        }
    });

}