Event to add product attribute to quote item, just once and not on sales_quote_item_set_product

You can try to use sales_quote_product_add_after.
That one is dispatched after you add a product to the cart.
the downside is that you get as parameter a list of all the items in the cart and you have to look for your latest item and set the attribute you need.
But you can easily identify it. It has the highest id.

Set this attribute as "Used for Promo Rules" = "Yes" at the attribute edit page admin > attributes > manage attributes and it will be available in the quote.

To get a product attribute as Amasty already mentioned you can also add it to this list:

app/code/core/Mage/Sales/etc/config.xml:1251 XPATH: /config/global/sales/quote/item/product_attributes 

Of course not in the Mage_Sales config.xml but in your own :-)

I have decided to use checkout_cart_product_add_after. This is dispatched right after a product is added to cart from:

Mage_Checkout_Model_Cart::addProduct($productInfo, $requestInfo=null)

I didn't want to use Amasty's or Fabian's approach because it would have an additional attribute load from the DB into the quote item's product whenever a quote item is loaded from the DB. I am rather looking to store the value in sales_flat_quote_item table after I've made that entry on add to cart.