If the cookie duration is low there is only one reason to use that advertiser (from an affiliates point of view). That is, they have products that you want to sell. Now these products should be very specific to your site and probably isn't too many. Anyway, what you have to do is make a page on your site that contains just these products. In general, you don't want to list the merchant at all. Make it seem like the customer is buying the product from you. This way, the customer, can leave and come back and buy later. When they buy they will use your links and you'll get the commission.
Cow and horse themed gifts