Javascript in update panel doesn't work after partial postback

Place your datetimepicker initialisation code in the pageLoad function, which is called whenever the page loads (asynchronously or synchronously).

<script type="text/javascript">
    function pageLoad(sender, args) {
        $('.datePicker').datetimepicker({ dateFormat: 'dd/mm/yy' });
    }      
</script>

You can use pageLoad or .live:

Reference info: $(document).ready() and pageLoad() are not the same

.live:

Jquery .live works but not with .datepicker

$(function(){
    $('.datePicker').live('click', function() {
        $(this).datepicker({showOn:'focus'}).focus();
    });
});

pageLoad():

function pageLoad(sender, args) {
    $('.datePicker').datetimepicker({ dateFormat: 'dd/mm/yy' });
}