Или попробуйте это за $ sql:
$sql_query2 = "UPDATE posts SET post_title = '.$post_title.', post_category = '.$post_category.', post_tags = '.$post_tags.', post_text = '.$post_text.', post_image = '.$post_image.', WHERE post_id = '.$_POST[post_id].'";
или
$sql_query2 = "UPDATE posts SET post_title = $post_title, post_category = $post_category, post_tags = $post_tags, post_text = '$post_text', post_image = $post_image, WHERE post_id = '.$_POST[post_id].'";