Problem displaying one post from each category

Question

I’ve checked this code localy, here is the working snippet:

        <?php
        $cat_args = array(
                'orderby' => 'name',
                'order' => 'ASC',
                );

        $fcategories =   get_categories($cat_args); 

        foreach($fcategories as $fcategory) {
            echo '<dl>';
            echo '<dt> <a href="' . get_category_link( $fcategory->term_id ) . '" title="' . sprintf( __( "View all posts in %s" ), $fcategory->name ) . '" ' . '>' . $fcategory->name.'</a></dt>';

            $post_args = array(
                    'posts_per_page' => 1,
                    'cat' => $fcategory->cat_ID
                    );

            $fposts = query_posts($post_args);

            while(have_posts()) : the_post();    ?>
                <dd><a href="<?php the_permalink(); ?>"><?php the_title(); ?></a></dd>
                <?php

                echo '<dd class="view-all"> <a href="' . get_category_link( $fcategory->term_id ) . '" title="' . sprintf( __( "View all posts in %s" ), $fcategory->name ) . '" ' . '>View all posts in ' . $fcategory->name.'</a></dd>';
            echo '</dl>';
            endwhile; 
        }
        wp_query_reset();
?>

Original answer:
I think the problem might be here:

$post_args = array(
  'showposts' => 1,
  'category' => $fcategory->cat_ID
);

you’re using category argument, it should be cat so try this code:

$post_args = array(
  'showposts' => 1,
  'cat' => $fcategory->cat_ID
);