Array
(
    [201303] => Array
        (
            [month_year] => March 2013
            [more_posts] => 1
            [posts] => Array
                (
                    [0] => Array
                        (
                            [post_title] => Test Post 1
                        )

                    [1] => Array
                        (
                            [post_title] => Test Post 2
                        )

                    [2] => Array
                        (
                            [post_title] => Test Post 3
                        )

                )

        )

    [201302] => Array
        (
            [month_year] => February 2013
            [more_posts] => 1
            [posts] => Array
                (
                    [4] => Array
                        (
                            [post_title] => Test Post 4
                        )

                    [5] => Array
                        (
                            [post_title] => Test Post 5
                        )

                    [6] => Array
                        (
                            [post_title] => Test Post 6
                        )

                )

        )
    ...
)

global $wpdb;
$blog_posts = array();
$num_months = 12;
$num_posts = 3;
$num_posts_buffer = $num_posts + 1;

$wpdb->query('set @row_num := 0, @month_year := \'\'');

$query = 'SELECT wpp3.ID, wpp3.post_title, wpp3.month_year, wpp3.month_year_slug ';
$query .= 'FROM (SELECT wpp2.*, ';
	$query .= '@row_num := IF(@month_year = month_year, @row_num + 1, 1) AS row_num, ';
	$query .= '@month_year := month_year ';
	$query .= 'FROM (SELECT wpp1.*, ';
		$query .= 'DATE_FORMAT(post_date, \'%%M %%Y\') AS month_year, ';
		$query .= 'DATE_FORMAT(post_date, \'%%Y%%m\') AS month_year_slug ';
		$query .= 'FROM ' . $wpdb->posts . ' AS wpp1 ';
		$query .= 'WHERE wpp1.post_status = %s ';
		$query .= 'AND wpp1.post_type = %s ';
		$query .= 'ORDER BY wpp1.post_date DESC';
		$query .= ') as wpp2';
	$query .= ') as wpp3 ';
$query .= 'WHERE row_num <= %d ';
$query .= 'LIMIT %d';

SELECT wpp3.id,
  wpp3.post_title,
  wpp3.month_year,
  wpp3.month_year_slug
FROM (
  SELECT wpp2.*,
    @row_num := IF(@month_year = month_year, @row_num + 1, 1) AS row_num,
    @month_year := month_year
  FROM (
    SELECT wpp1.*,
      Date_format(post_date, '%M %Y') AS month_year,
      Date_format(post_date, '%Y%m') AS month_year_slug
    FROM wp_posts AS wpp1
    WHERE wpp1.post_status = 'publish'
      AND wpp1.post_type = 'post'
    ORDER BY wpp1.post_date DESC
  ) AS wpp2
) AS wpp3
WHERE row_num <= 4
LIMIT 48;

SELECT wpp1.*,
      Date_format(post_date, '%M %Y') AS month_year,
      Date_format(post_date, '%Y%m') AS month_year_slug
FROM wp_posts AS wpp1
WHERE wpp1.post_status = 'publish'
      AND wpp1.post_type = 'post'
ORDER BY wpp1.post_date DESC

SELECT wpp2.*,
  @row_num := IF(@month_year = month_year, @row_num + 1, 1) AS row_num,
  @month_year := month_year
FROM (
  # Query from section 3.1 here
) AS wpp2

SELECT wpp3.id,
  wpp3.post_title,
  wpp3.month_year,
  wpp3.month_year_slug
FROM (
  # Query from section 3.2 here
) AS wpp3
WHERE row_num <= 4
LIMIT 48;

$posts = $wpdb->get_results(
	$wpdb->prepare(
		$query,
		'publish', 'post', $num_posts_buffer, ($num_months*$num_posts_buffer)
	),
	ARRAY_A
);

// If there are blog posts to loop through
if(!empty($posts)) {

	// Start our counter at zero
	$index = 0;

	// Create a variable to keep track of whether we need to continue looping
	$continue_looping = true;

	// If we need to continue looping and the current post exists
	while($continue_looping && isset($posts[$index])) {

		// Store the current post
		$post = $posts[$index];

		// Assume there are no more posts in this month
		$more_posts = false;

		// If this particular month/year doesn't exist
		if(!isset($blog_posts[$post['month_year_slug']])) {

			// We know this is the first post in the month
			$num_posts_month = 1;

			// If we have posts for all $num_months, we know we're done
			if(count($blog_posts) >= $num_months) {

				// Remember that we're done looping now
				$continue_looping = false;
			} else {

				// Create a new month in our array and save the month/year
				$blog_posts[$post['month_year_slug']]['month_year'] = 
				$post['month_year'];

				// Assume and save that there are no additional posts
				// in the database for that month
				$blog_posts[$post['month_year_slug']]['more_posts'] = false;
			}
		} else {

			// We know this is an additional post in that month
			$num_posts_month++;
		}

		// If we should continue looping at this point
		if($continue_looping) {

			// If we need more posts for this month
			if($num_posts_month <= $num_posts) {

				// Get the permalink for this post
				$permalink = get_permalink($post['ID']);

				// Save this post in our array
				$blog_posts[$post['month_year_slug']]['posts'][$index]['post_title'] =
				'<a href="' . $permalink . '">' . $post['post_title'] . '</a>';
			} else {

				// Record that there are actually more posts
				// in the database then we can display
				$blog_posts[$post['month_year_slug']]['more_posts'] = true;
			}
		}

		// Increment post index
		$index++;
	}
}

return $blog_posts;