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.
Yup, I may have a few old pages that mention merchant names but any new pages I've been putting up in the last year or so never mention the mechant by name. No need to give the name as it just adds to unpaid "branding" for the merchant in respect of those who visit my pages and don't click through. It may sound harsh but yes, I'd rather people remember my site's name than the merchant's, particularly when you take "keep=no" cookies into consideration.