Select box saves but doesn’t update value in admin

The second parameter of selected() has to agree with the value attribute of the current <option>. So assuming you have stuffed $selected with the value given by the relevant get_post_meta(), the following should work for you:

<label for="myplugin_meta_box_select">Status:</label>
<select name="myplugin_meta_box_select" id="myplugin_meta_box_select">
  <option value="Approved" <?php selected( $selected, 'Approved' ); ?>>Approved</option>
  <option value="In Progress" <?php selected( $selected, 'In Progress' ); ?>>In Progress</option>
</select>

Side note: I’d personally prefer to use the “sluggish” version (i.e. inprogress instead of In Progress) for the value attribute (and thus for the post meta value), but you’d have to make changes to your front-end as well.