Fields don’t reflect previous Quick Edit changes when clicking Quick Edit a second time

The solution was on the jquery side of things. The .on function needed to bubble upwards to be sure that it was always getting the most recent, ajax-added content. I only had to adjust the first line to be more aligned with jquery documentation for .on().

$( '#the-list' ).on( 'click', '.editinline', function(){

    // revert Quick Edit menu so that it refreshes properly
    inlineEditPost.revert();

    posttitlelabel = $( ':input[name="post_title"]', '.inline-edit-row' ).parents( 'label' ); 
    tag_id = $( this ).parents( 'tr' ).attr( 'id' );    
    subtitle = $( 'div.kia-subtitle-value', '#' + tag_id ).text();  

    $( 'input.kia-subtitle-input', '.inline-edit-row' ).val( subtitle ).parents( 'label' ).insertAfter( posttitlelabel );

});