Get_theme_mod not retrieving value

Question

It is really simple. set_theme_mod

File: /wp-includes/theme.php
889: function set_theme_mod( $name, $value ) {
890:    $mods = get_theme_mods();
891:    $old_value = isset( $mods[ $name ] ) ? $mods[ $name ] : false;
892: 
893:    /**
894:     * Filters the theme mod value on save.
895:     *
896:     * The dynamic portion of the hook name, `$name`, refers to the key name of
897:     * the modification array. For example, 'header_textcolor', 'header_image',
898:     * and so on depending on the theme options.
899:     *
900:     * @since 3.9.0
901:     *
902:     * @param string $value     The new value of the theme mod.
903:     * @param string $old_value The current value of the theme mod.
904:     */
905:    $mods[ $name ] = apply_filters( "pre_set_theme_mod_{$name}", $value, $old_value );
906: 
907:    $theme = get_option( 'stylesheet' );
908:    update_option( "theme_mods_$theme", $mods );
909: }

will save into the options table theme_mods_$theme where $theme is your theme name. But this will not happen until you press the Save & Publish Customizer button.

The preview page is like a dream land (Lat: Et est fallacia lunae).
Whatever you do the values will not be saved to the database.
And I think this is the only issue you are facing.

I duped what you have on your end.
I can confirm I can save the values every time.

function _20161230_customize_register( $wp_customize ) {

    $active_type="home";

    $wp_customize->add_section( $active_type. 'just_listed' , array(
            'title'      => __( 'Just Listed Settings', 'microformata' ),
            'priority'   => 53,
    ) );  

    $wp_customize->add_setting($active_type.'_categories_max',array(
            'default'      => '10',
            'transport'    => 'refresh'
            ));

    $wp_customize->add_control( $active_type.'_categories_max',array(
            'type' => 'select',
            'label' => 'Max Items',
            'section' => $active_type.'just_listed',
            'choices' => array(
                    '5' => '2',
                    '10' => '10',
                    '15' => '15',
                    '20' => '20',
                ),
            )); 
}

add_action( 'customize_register', '_20161230_customize_register' );

The Ajax result will be like this:

{success: true, data: {setting_validities: {home_categories_max: true}, changeset_status: "publish",…}}
data
:
{setting_validities: {home_categories_max: true}, changeset_status: "publish",…}
changeset_status
:
"publish"
next_changeset_uuid
:
"4b1ac702-3ae2-422d-875a-a02b6f5b2d65"
setting_validities
:
{home_categories_max: true}
success
:
true

What I am not sure, can you disable plugins you use and then test.
I know you use 4.7, because of the error message you got.

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