Destroy the datepicker's instance when you don't want it and create new instance whenever necessary.
I know this is ugly but only this seems to be working...
$("#ddlSearchType").change(function () {
if ($(this).val() == "Required Date" || $(this).val() == "Submitted Date") {
$("#txtSearch").datepicker();
}
else {
$("#txtSearch").datepicker("destroy");
}
});