Is this a sustainable business model? I am not sure. I do know you sometimes hear horror stories about sites like that. Generally, they have to do with the stampede effect created by Groupon and LivingSocial. As opposed to restaurant.com, which will give businesses a random amount of business, Groupon and LivingSocial tend to bring a stampede of business in around the same time. Some companies report regular customers being driven away by deal-seekers.
These sites do allow businesses to limit the amount of purchases (see Groupon terms here). However, businesses sometimes underestimate the demand for deal-seekers. For example, a British bakery recently offered a deal for a dozen of their gourmet cupcakes for $10. This was 75% off their normal price. This bakery chose to do all the deals at once (link to article), rather than spreading them out over a few weeks, and also chose not to cap the number of purchases, which many companies do. The normal monthly sale volume was around 1,200 cupcakes a month, they ended up making about 102,000. The owner had to bring in temporary workers just to meet their end of the bargain.
Now, could Groupon do a better job helping the customer avoid disasters like this? I am sure they could. However, the bakery owner also has to realize that caps exist for a reason, and should have seen the potential issue with opening it up to everyone with no restriction. That said, you have to feel for the owner who made this decision and cut in to what was likely a thin profit margin.