Coupon users are price-sensitive and this might be the only way to make them buy again. So why don't you give them coupons regularly to stimulate purchases? You could do other promotions for the customers who don't use coupons.
With Metrilo, you see all coupons you've used to acquire new customers for your business historically. Then you can select any of these customer cohorts and send them an email with a new coupon.
How to identify heavy coupon users and send them special email offer
From the main menu, go to the Retention.
From the breakdown menu under the graph, select Customer cohorts based on first purchase: Coupon.
Look at the cohorts and choose one or a few that make sense for such an email campaign.
Now that you know who you're going to target, go to People.
Start filtering customers by Action -> coupon used -> type in the name of the coupon you've chosen -> click on it. (As you start typing the coupon name, you'll get autofill suggestions to find it easily.)
You get a list of all customers who used this coupon. You can immediately send them an email with a coupon to re-engage them (the Email button on top of the page).
Here's an example email you can adapt to your business: