Depending on your theme, the discount code may not appear obviously on Mobile devices like it does on desktop. It is is hidden behind a little blue link that says something like “show order summary”. The customers have to click that blue “show order summary” link and then they will see their cart items and the coupon/discount code box. So if these customers are having trouble, find out if they are using a mobile device. They just have to click that link and it will appear. It’s a little silly but that’s how my theme appears on Mobile devices. We have to do a lot of explaining to customers.
The problem we had was to do with an add-on app B2B Commerce that lets some wholesale customers get a discounted price automatically without a code. Since that app processed the orders a little differently by creating a draft order, when these customers got to the checkout page the coupon box would not appear for them. It had to do with the B2B app, not shopify. Wouldn’t let them apply an additional discount or coupon or points.