Is each issue of a magazine site a static page

If you do not want to use the buildin archives, your best way of achieving this is to create a Page Template containing nearly the same code as the archive.php.

Also, add some post_meta to your static pages, containing the Year and Month of the posts you want to show.

In your page template, set up a custom query containing the restriction for the date, with the $args:

$args = array (
    'year' => get_post_meta( get_the_ID(), 'your_year_meta', true ),
    'monthnum' => get_post_meta( get_the_ID(), 'your_month_meta', true )
    'offset' => $offset,
    //...
);

Make the query as usual, and use the code from your archive.php to loop through the posts.

Also make sure that, if you want your posts paginated, you calculate the custom offset right, and this should be it 🙂