I've spoken with a few business owners who have run Groupon promotions - primarily entertainment, fitness and restaurant businesses, so I'm not sure if my thirdhand knowledge is applicable.
In short, all of them said they would "probably" not do it again. The issue, as others mentioned, is you bring in customers that are unlikely to return after the deal is over and they aren't very good at spreading word of mouth either.
The bigger complaint though is around the quality of service that existing, loyal patrons receive during the promotions. For example, a local yoga studio was overwhelmed with new customers during a promotion, resulting in very full classes with very little room and even less personal attention. Imagine you're a loyal, long term customer paying full price and you show up to have to squeeze in to a room of newbies who have no idea what they're doing. You might be pretty upset.
So, my thoughts are that in addition to making sure you have a plan in place to convert the deal seekers, is to ensure that you don't alienate or tick off your existing customer base as well. I can't imagine a worse scenario than losing your loyal fan base in an attempt to bring in new (and almost certainly temporary) business.