使用admin-ajax.php的AJAX请求

I'd be really surprised if you managed to make those Ajax action hooks work inside an Output Buffer.
AFAIK, we should only use PHP ob_* functions as last resort.

Here's a standard implementation. A JavaScript file will be enqueued inside the shortcode callback function, and inside it we fire a document.ready Ajax call. The admin-ajax.php URL is passed to a JS object using wp_localize_script. Check the code comments for more info and the Codex for details on each WP function:

<?php
/**
 * Plugin Name: (SO) Simple Ajax Shortcode
 * Description: Fire an Ajax action when rendering a shortcode
 * Author:      brasofilo
 * Plugin URL:  https://stackoverflow.com/a/22585520/1287812
 */

add_shortcode( 'testshortcode', 'shortcode_so_22579460' );
add_action( 'wp_enqueue_scripts', 'enqueue_so_22579460' );
add_action( 'wp_ajax_Test_SO', 'Test_SO' );
add_action( 'wp_ajax_nopriv_Test_SO', 'Test_SO' );

/**
 * Enqueue our script inside the shortcode 
 */
function shortcode_so_22579460($attributes)
{
    wp_enqueue_script( 'my-script' );
    return '<h1>Check the broswer console.</h1>';
}

/**
 * Register and localize our script
 */
function enqueue_so_22579460() 
{
    wp_register_script( 
         'my-script',
         plugin_dir_url( __FILE__ ) . 'ajax.js',
         array( 'jquery' ) // enqueue jQuery as dependency
    );

    // We can pass any number of PHP data to the JS 'wp_ajax' object
    // Here, only the basics, Ajax URL and a security check 
    wp_localize_script( 
        'my-script', 
        'wp_ajax',
        array( 
              'ajaxurl'     => admin_url( 'admin-ajax.php' ),
              'ajaxnonce'   => wp_create_nonce( 'ajax_post_validation' ) 
         ) 
    );
}

/**
 * Ajax callback
 */
function Test_SO()
{
    // Security check
    check_ajax_referer( 'ajax_post_validation', 'security' );

    // Demonstrative boolean value to return
    $random = ( rand() % 2 != 0 );

    if( $random )
        wp_send_json_error( array( 'error' => 'Random is ODD' ) );
    else
        wp_send_json_success( 'Random is EVEN' );
}

And the JavaScript file (ajax.js) stored in the same folder as the plugin file:

jQuery(document).ready( function($) 
{
    var data = {
        action: 'Test_SO',
        security: wp_ajax.ajaxnonce
    };

    $.post( 
        wp_ajax.ajaxurl, 
        data,                   
        function( response )
        {
            // Errors
            if( !response.success )
            {
                // No data came back, maybe a security error
                if( !response.data )
                    console.log( 'AJAX ERROR: no response' );
                // Error from PHP
                else
                    console.log( 'Response Error: ' + response.data.error );
            }
            // Success
            else
                console.log( 'Response Success: ' + response.data );
        }
    ); 
});

_{Here's a similar answer of mine using OOP and jQuery commands to trigger the action. And an article of interest.}