I think the business model of Groupon is sustainable.
This is my guess and I base my answer on the assumption, that for this model to be sustainable, both parties (I mean companies that sell goods and services, as well as people who buy them) have to have the interest in using Groupon (or similar site).
In first case, the companies selling goods, if you have some excess goods (be it some rooms in the hotel or some older models of your products), you can either destroy them (good), do not use (hotel rooms) or sell them with a lower price. If Groupon or similar site has a large base of users, it is a good way to sell these excessive products / services - you then have quick group targeted at responding deals with high discounts.
When it comes to the buyers, as long as they see the offers that interest them (especially when it is economic downturn, when the price matters more), they will be using the site. Of course in this case the user loyalty somehow should be sustained (preferably binding people with the site, like Facebook binds users with their site), but it is a different question.
So, to sum up, in my opinion this business model can be sustained, but will have to adapt to function after the initial hype will stop. Even if Groupon and its clones will fail to do that, they will not vanish quick, because it will change gradually, I think.
Read about current projections on how the daily deal market will rise:
Forbes: Who Will Be Left Standing Post-Groupon IPO