CSC no longer available - need to reauthorize

We occasionally have situations whereby we have taken and order and then for one of many reasons, the order value increases. 

We use the pre-authorization at time of order, which works fine.   The customer has by then entered verified CC information including address, CSC, etc.  Later in the process, the value of the order increases through an add of an item or a customer change of an item.  The authorization, however, is still valid only for the smaller original amount.  If we then attempt to bill the higher value order prior to shipment, it fails - not because the charge card has insufficient credit available, but because the new amount exceeds the original amount.