Generally it has taken a savvy owner to make it work for them. Non-savvy owners would get over-sold by the deals sales reps. At the height of the deals craze, small business owners were getting 5 calls a day from various deals sites.
What Groupon never figured out is how to make a sales organization that wouldn't burn out merchants. So now they're pivoting into being Woot.
I would love to see how many times a business that tried groupon after the first time.
They have tended to be places like paintballing or sky diving, things where the cost doesn't go up that much more with the more people who come. And who can upsell (paintballs, photographs). There's a technical business term for those businesses that I can't remember.
But apparently they do do well out of groupon.
Anything with inventory costs (e.g. restaurants) have a much harder time. Food costs are a significant portion of the cost of serving a table. It wouldn't be bad to have a loss-leader for one or two meals, but grouponers don't become "the next repeat customer", so you just lose money on the meals with not much to show.
A business can make money off a Groupon deal if you don't think of it as a loss leader (since it will just wind up being a loss). You're not going to acquire new customers and they'll likely never come back without you offering another deal, so think of them as a one-time customer and make money off that one visit. It will only work for very high margin businesses where you can upsell a lot of add-ons. And only if you price it so you make money, even just a little bit, if the customer doesn't buy any of those add-ons.