If you are unable to use a one-time-per-person coupon when reordering an order after cancelling it on Shopify, you can use the "Edit Discount & Refund" process in the reorder details

When a customer cancels an order on Shopify for some reason and then places a new order, there are cases where the coupon that was used once cannot be used. In such cases, we ask the customer to place the order as usual, then manually edit the discount on the order and reapply it.