The merchant should NOT have run the promotion at a LOSS. The promotion should have been at least break even, if not slightly profitable.
Groupon seems to demand at least a 50% discount on normal prices, and then seems to want to take between 50 and 100% of the actual groupon coupon cost. That leaves the merchant able to collect somewhere between 0 and 25% of their standard pricing. Other than software businesses, there are few few shops that have enough of a markup to be able to sell something at 25% of face value and still make money on the product itself, much less cover all the additional overhead.
Bashing your head against a brick wall hurts, but the solution isn't to find the least painful brick, it's to stop bashing.