Product characteristics

-- url of the page with the problem -- : sushi-cours.lu
-- HikaShop version -- : business 2.2.1
-- Joomla version -- : 3.2.1
-- PHP version -- : 5.3.16
-- Browser(s) name and version -- : XXXXX x.x.x
-- Error-message(debug-mod must be tuned on) -- : Error_message

I have a product with multiple characteristics.
for example : Cooking class has 4 characteristics, for example :

1. March 1,2014
2. March 2, 2014
,
3. March 3,2014
,
4. March 4,2014
[/lol]

When I go to the product "cooking Class" and manage the characteristics, it works perfectly and the customer can nicely chose the characteristics on the frontpage.
But
when i return to the product/characteristics manager, and i unpublish an item, it is still available for being chosen as a characteristics by the costumer on the frontend. So i need, each time, to go the the main menu/characteristics and delete the characteristics.

that's not cool ! it should not be in the dropdown menu, once unpublished in the characteristics manager of the product