Unfortunately, our system has no way to track "remaining value" for any individual cart discount code.
If it's set as a 1x-use code, then it can be used exactly once. If you also did not require a Minimum Order Amount for that discount code, and if the order total was less than the discount amount, then the code would be accepted but any discount remainder beyond the actual order total would be forfeited.
If there was some misunderstanding in this regard between you and your customer, perhaps you could create a special discount code good for the remaining amount and only disclosed to the affected customer for their personal use.
