If you're going to give discounts, bonus offers, or otherwise incentivize customers, your repeat customers should get the same deals (or better).
I'm still surprised at how many companies don't do that and treat new customers better than their loyal customers.
You'd expect bad behavior from cell phone carriers and other forced-monopolies but not in ecommerce where a customer can click and tap over to your competitor to get a better deal.
If you don't discount or a time-limited offer expired, you don't need to do anything special for repeat customers. It would be nice if you can, but optional.
But if you do use coupons or the like, make sure loyal customers can too.
Upsetting and burning a repeat customer is a sure-fire way to get them to spread bad word of mouth about your business. You'd be losing customers you didn't even know you lost.
Repeat Customer Insights might be able to highlight some of those customers though.
In the Customer Grid there is a Defected loyal and Defection risk loyal segment that contain customers who used to by frequently but suddenly stopped.
If you're worried about losing customer, it's worth the time trying to get in touch with them and asking why they stopped buying. It could be a discount problem like above or many a missed expectation with a product.
Learn what your customers are actually doing instead of just guessing
One of the best ways to build a sustainable business starts by getting your customers to come back. Mastering that simple process can be difficult, but builds a lifelong business.
Repeat Customer Insights can help you understand your customer's behavior. With its collection of behavior reports, you can see what they're actually doing instead of guessing and having your efforts fall flat.