Preserve custom URL parameter on more pages

You will need to intercept the links generated by WordPress and append the query var onto the relevant URLs.

You can do this quite easily with a filter on category URLs with something like…

function add_my_query_var( $link ) {
    $link = add_query_arg( 'sort', 'most_voted', $link );
    return $link;
}
add_filter('category_link','add_my_query_var');

I also spotted this handy list of filters on Mike’s post on SO, it should cover all the possible URLs you’d want to tweak the query vars for…

add_filter('page_link','add_my_query_var');
add_filter('post_link','add_my_query_var');
add_filter('term_link','add_my_query_var');
add_filter('tag_link','add_my_query_var');
add_filter('category_link','add_my_query_var');
add_filter('post_type_link','add_my_query_var');
add_filter('attachment_link','add_my_query_var');
add_filter('year_link','add_my_query_var');
add_filter('month_link','add_my_query_var');
add_filter('day_link','add_my_query_var');
add_filter('search_link','add_my_query_var');

add_filter('feed_link','add_my_query_var');
add_filter('post_comments_feed_link','add_my_query_var');
add_filter('author_feed_link','add_my_query_var');
add_filter('category_feed_link','add_my_query_var');
add_filter('taxonomy_feed_link','add_my_query_var');
add_filter('search_feed_link','add_my_query_var');

add_filter('get_edit_tag_link','add_my_query_var');
add_filter('get_edit_post_link','add_my_query_var');
add_filter('get_delete_post_link','add_my_query_var');
add_filter('get_edit_comment_link','add_my_query_var');
add_filter('get_edit_bookmark_link','add_my_query_var');

add_filter('index_rel_link','add_my_query_var');
add_filter('parent_post_rel_link','add_my_query_var');
add_filter('previous_post_rel_link','add_my_query_var');
add_filter('next_post_rel_link','add_my_query_var');
add_filter('start_post_rel_link','add_my_query_var');
add_filter('end_post_rel_link','add_my_query_var');

add_filter('previous_post_link','add_my_query_var');
add_filter('next_post_link','add_my_query_var');

add_filter('get_pagenum_link','add_my_query_var');
add_filter('get_comments_pagenum_link','add_my_query_var');
add_filter('shortcut_link','add_my_query_var');
add_filter('get_shortlink','add_my_query_var');

add_filter('home_url','add_my_query_var');
add_filter('site_url','add_my_query_var');
add_filter('admin_url','add_my_query_var');
add_filter('includes_url','add_my_query_var');
add_filter('content_url','add_my_query_var');
add_filter('plugins_url','add_my_query_var');

add_filter('network_site_url','add_my_query_var');
add_filter('network_home_url','add_my_query_var');
add_filter('network_admin_url','add_my_query_var');

Hope that helps..