Just use the selected
argument:
wp_dropdown_categories( array(
'show_option_all' => 'All Deployments',
'hierarchical' => true,
'show_count' => true,
'selected' => get_query_var( 'cat' ),
));
Update: Hook onto the tag_link
filter & add the current category (if applicable):
add_filter( 'tag_link', 'wpse_71874_tag_link_category_context' );
function wpse_71874_tag_link_category_context( $link ) {
if ( is_category() && $cat_id = get_queried_object_id() )
$link = add_query_arg( 'cat', $cat_id, $link );
return $link;
}