They seem to have a high acquisition cost for deals. Many merchants have already been burnt by them - they often make a hefty loss, so acquisitions get harder. You could also argue that most of the merchants using Groupon are already businesses on the downturn, so they will only use Groupon once and not see any gain from it since their business was unpopular to begin with, and the only way customers would be somewhat satisfied with the experience is at a price discount the business simply cannot survive on.

Perhaps Groupon could do some better segmentation of their users. They must have quite a lot signed up, so why not offer many more deals overall, and each user gets the three deals he is most likely to buy. Also, you take a much smaller portion of the revenue so the business can survive. This way, Groupon would earn more through increased volume (it is kind of unprofessional to send a customer a similar deal six times a month - if I didn't buy it before why waste your reach to show it again to me?) In essence they would be a highly-tailored ad agency getting a small commission on a huge number of sales.