“Current” class on a singular page menu item with custom post types?

Given that the markup of your menu does not seems to generating all of the classes I’d expect to see, I’ll guess at the problem.

  1. Your theme is using a custom Walker
  2. Or something– theme or plugin– has added a filter to (probably)
    wp_nav_menu_css
    .
  3. Though there are other filters that could be used.

To fix it, or try to, make sure your theme does not include a walker argument when it calls wp_nav_menu and search your theme and plugins for wp_nav_menu_css and other relevant filters.

If it is a walker you can remove that walker argument, though it may effect other theme functionality. If it is a filter it can be removed with remove_filter()