Pagination not working in some author pages

Question

I have an author archive page to display authors' posts. In some of the authors the pagination works, but in some cases it doesn't.

Where is the problem? Here is my code:

<?php
$paged = (get_query_var('page')) ? get_query_var('page') : 1;
$wpfp_before = "";
echo "<div class='wpfp-span'>";

if ($wpfp_before):
echo '<div class="wpfp-page-before">'.$wpfp_before.'</div>';
endif;
$favorite_post_ids = get_user_meta($user_id, 'wpfp_favorites', true);
if ($favorite_post_ids) {
$favorite_post_ids = array_reverse($favorite_post_ids);
$post_per_page = wpfp_get_option("post_per_page");
$page = intval(get_query_var('paged'));

$qry = new wp_query(array('post_type' => 'videosprogram' ,  'post__in' => $favorite_post_ids ,'posts_per_page' => 3,'paged' => $paged ) );                      

while ($qry->have_posts() ) : $qry->the_post();


//Loop ....


endwhile; wp_pagenavi( array( 'query' => $qry ) ); ?>

UPDATE:-

i try this way :-

function cpt_on_author_page( $query ) {
    $curauth = (isset($_GET['author_name'])) ? get_user_by('slug', $author_name) : get_userdata(intval($author));
    //$author_name = get_post_meta($curauth->id, 'author_name', true);
    if ( $query->is_author() && $query->is_main_query() ) {
        $query->set( 'post_type', 'videosprogram' );
        $query->set( 'posts_per_page', 1 );
        $query->set( 'meta_key' , 'show_program_editors');
        $query->set( 'meta_value' , $curauth->id); 


    }
}
add_action( 'pre_get_posts', 'cpt_on_author_page' );

but not show me any post