function my_date_archive_for_category() {

...
$page = (get_query_var('paged')) ? get_query_var('paged') : 1;
	query_posts(array(
		'cat' => $category_array["term_id"],
		'year'=> $request_parts["4"],
		'monthnum'=>$request_parts["5"],
		'paged' => $paged
	));

	if ( have_posts() ) :

	  while ( have_posts() ) : the_post(); ?>
		<div <?php post_class() ?>>
<?php global $post; ?>

	<?php endwhile; ?>

<?php if(function_exists('wp_pagenavi')) { wp_pagenavi(); } ?>
<?php		
	else:
		$is404 = true;
	endif;
		}
	else {
		$is404 = true;
	}
	}
	else {
		$is404 = true;
	}

	if($is404) {
		include(TEMPLATEPATH . '/404.php');
		} ?>
	</div><!--end for left-r-->

	</div>

	<div id="right">
		<?php get_sidebar(); ?>
	</div>

	</div>

<?php get_footer();
		exit;
	}
}

add_action('init','my_date_archive_for_category');

Solution - 1

after the function query_posts run please make

var_dump($GLOBALS['wp_query'])

Solution - 2

Looks like a simple typo maybe?

$paged = (get_query_var('paged')) ? get_query_var('paged') : 1; query_posts(array( 'cat' => $category_array["term_id"], 'year'=> $request_parts["4"], 'monthnum'=>$request_parts["5"], 'paged' => $paged ));