Enable/Disable datepicker using jquery in mvc.

$("#txtcurrentdate").datepicker("enable");
$("#txtcurrentdate").datepicker("disable");
This disables the entire textbox. So may be you can use datepicker.destroy() instead:

$(document).ready(function() {
    $("#ddlsearch").change(function() {
        if ($(this).val() == "Required Date" || $(this).val() == "Submitted Date") {
            $("#txtcurrentdate").datepicker();
        }
        else {
            $("#txtcurrentdate").datepicker("destroy");
        }
    }).change();
});