The problem is that you are adding the click code to the changeYes button every time the popup is launched. You should only add it once outside of the div click:
Updated FIDDLE
$("#US_toggle").click(function () {
$('#US_Popup').popup('open');
});
$('#US_changeYes').click(function () {
if ($("#US_toggle .ui-flipswitch").hasClass('ui-flipswitch-active')) {
$("#US_toggle .ui-flipswitch").removeClass('ui-flipswitch-active');
} else {
$("#US_toggle .ui-flipswitch").addClass('ui-flipswitch-active');
};
});
UPDATE: Instead of toggling the classes, it is probably better to toggle the select value and then refresh the flipswitch:
$('#US_changeYes').click(function () {
var curVal = $("#US_flipswitch").val();
curVal == "off" ? $("#US_flipswitch").val("on").flipswitch("refresh") : $("#US_flipswitch").val("off").flipswitch("refresh");
});
New FIDDLE