For example: http://posiescafe.com/wp/?p=316 The deal was $6 for $13 worth of merchandise, but after Groupon's take, she gets to keep $3. No way to cover costs with a deal like that.. never mind profit.
And if the deal is unprofitable, there's no way to economically justify the offering unless you start factoring in soft effects like return visiters, name recognition, etc.