Almost any business should be willing to lose a little on product if that loss displaces more in other promotion/customer-acquisition costs. A business would be more willing to do so if they're sure the cost is reaching new customers. Perhaps that's an important part of the Groupon secret sauce -- the purchase of the 'coupon' with credit cards that provide a relatively strong identity signal. That could be used -- eventually, at least -- to target future promotions to unique new customers.
Does anyone know what sort of data the business gets from Groupon? Have any businesses offered repeat Groupons that aren't available to people who bought the first one?