Really when it comes to coupons there are three options that actually work. You can always have a sale, you can make it a pain to use, or you can limit yourself to 10 to 15% off.
Giving discounts may induce the most price sensitive to use your service. They will continue to be price sensitive, and stop using your service once the cost returns to normal.
If the opposite were true, and if business actually did profit from this approach, then it is likely that Groupon would be killing it.
At the end of the day, some types of retailers find ways to profit even off of the price sensitive, but it seems to be the case that the same is not true for most Groupon-trying businesses.
This has been a key part of the mailing list business for many years -- lists that target people who have recently moved, gotten pregnant or had a baby, gotten married, and so on. Special offers with unusually good deals are then offered, because the chance of converting a percentage of the recipients into long-term customers makes it worth it.
If this kind of business model has been translated to online effectively, I'm not familiar with it. Certainly some of that effect can be achieved with the right search keywords or the right websites to advertise on (e.g. baby name sites), but businesses like Groupon and Living Social have brought in many more price sensitive customers than actual long-term business prospects, which is one of the big reasons why they are not more successful.