A payment for post purchase offers can fail in some cases (for example: insufficient funds, CC errors, etc).
If customers accept an offer but runs into a payment failure, they will be directed to the thank you page and prompted to enter payment again to accept the post-purchase offer.
In addition, customers will receive an email from Shopify letting them know payment is needed to complete the order.
On your orders list, the order will show as a partially paid order. To handle the situation, you can potentially:
* Collect the payment (through the checkout link Shopify provides)
* Edit the order manually to remove the unpaid item
* Refund the order
Another possible reason for a partially paid order is capturing payments manually.
In this case, a payment must be manually captured for the original order as well as any post-purchase offers before the order status will update to paid.