Making jQuery .change() event persistent after widget save

The form reloads itself each time you save returning to the initial state where all are shown. What you can do is this:

// Getting the value of the selected field
var my_select_value = $('#widgets-right select.my-select').val();

// If there's no value selected, hide everything.
if(my_select_value == 0){
    $('.widget-test .row').hide();
}
// Otherwise, show the specific rows
if(my_select_value == 1){
    $('.widget-test .row').hide();
    $('.widget-test .row.one').show();
}
if(my_select_value == 2){
    $('.widget-test .row').hide();
    $('.widget-test .row.two').show();
}
if(my_select_value == 3){
    $('.widget-test .row').hide();
    $('.widget-test .row.three').show();
}

At the initial stage of the JavaScript.