Hi,
If you edit the file "show" of the view "order", you'll see that line:
if( $this->config->get('print_invoice_frontend') && !in_array($this->element->order_status,array('created','refunded','cancelled'))){ ?>
So the invoice will be available on the order details page as long as the order status is different than created, refunded and cancelled.
It doesn't take into account the order invoice statuses option of the configuration.
So just add the name of your status in that code and it will work like you want.