'depth'=>-1 will show all the levels (source^):

$depth
(integer) (optional) How many levels of the hierarchy are to be included where 0 means all. -1 displays links at any depth and arranges them in a single, flat list.
Default: 0

So your code will be:

<?php if (has_nav_menu( 'secondary' )) { 
    wp_nav_menu( array(
    'container'         => '', 
    'menu_class'        => '', 
    'menu_id'           => 'menu-header-menu', 
    'items_wrap'        => '<ul id="%1$s">%3$s</ul>',
    'depth'             => -1,
    'theme_location'    => 'secondary' ) );
}

And DRY - Don't Repeat Yourself. As the default value of fallback_cb is wp_page_menu, you don't need to repeat it. So do the container_class. And there's no such sort_column parameter in wp_nav_menu().

###EDIT### You must put

register_nav_menus( array( 'secondary'=>__('Secondary Menu', 'text-domain') ) );

in your functions.php register the nav menu so that you can assign your menu to this location. Even though you create a new menu from Appearance » Menus, if you not assign it to the desired location, then you can't enable it to there.

'depth'=>-1 will show all the levels (source^):

$depth
(integer) (optional) How many levels of the hierarchy are to be included where 0 means all. -1 displays links at any depth and arranges them in a single, flat list.
Default: 0

So your code will be:

<?php if (has_nav_menu( 'secondary' )) { 
    wp_nav_menu( array(
    'container'         => '', 
    'menu_class'        => '', 
    'menu_id'           => 'menu-header-menu', 
    'items_wrap'        => '<ul id="%1$s">%3$s</ul>',
    'depth'             => -1,
    'theme_location'    => 'secondary' ) );
}

And DRY - Don't Repeat Yourself. As the default value of fallback_cb is wp_page_menu, you don't need to repeat it. So do the container_class. And there's no such sort_column parameter in wp_nav_menu().

EDIT

You must put

register_nav_menus( array( 'secondary'=>__('Secondary Menu', 'text-domain') ) );

in your functions.php register the nav menu so that you can assign your menu to this location. Even though you create a new menu from Appearance » Menus, if you not assign it to the desired location, then you can't enable it to there.

'depth'=>-1 will show all the levels (source^):

$depth
(integer) (optional) How many levels of the hierarchy are to be included where 0 means all. -1 displays links at any depth and arranges them in a single, flat list.
Default: 0

So your code will be:

<?php if (has_nav_menu( 'secondary' )) { 
    wp_nav_menu( array(
    'container'         => '', 
    'menu_class'        => '', 
    'menu_id'           => 'menu-header-menu', 
    'items_wrap'        => '<ul id="%1$s">%3$s</ul>',
    'depth'             => -1,
    'theme_location'    => 'secondary' ) );
}

And DRY - Don't Repeat Yourself. As the default value of fallback_cb is wp_page_menu, you don't need to repeat it. So do the container_class. And there's no such sort_column parameter in wp_nav_menu().

'depth'=>-1 will show all the levels (source^):

$depth
(integer) (optional) How many levels of the hierarchy are to be included where 0 means all. -1 displays links at any depth and arranges them in a single, flat list.
Default: 0

So your code will be:

<?php if (has_nav_menu( 'secondary' )) { 
    wp_nav_menu( array(
    'container'         => '', 
    'menu_class'        => '', 
    'menu_id'           => 'menu-header-menu', 
    'items_wrap'        => '<ul id="%1$s">%3$s</ul>',
    'depth'             => -1,
    'theme_location'    => 'secondary' ) );
}

And DRY - Don't Repeat Yourself. As the default value of fallback_cb is wp_page_menu, you don't need to repeat it. So do the container_class. And there's no such sort_column parameter in wp_nav_menu().

###EDIT### You must put

register_nav_menus( array( 'secondary'=>__('Secondary Menu', 'text-domain') ) );

in your functions.php register the nav menu so that you can assign your menu to this location. Even though you create a new menu from Appearance » Menus, if you not assign it to the desired location, then you can't enable it to there.