Could invoices have been posted with a date that old? Or perhaps these invoices were posted many years ago, but not cleared when paid because the payments were not applied to the invoices?

If an invoice has a current amount not equal to zero, it will not get cleared to history, even if there is a payment on the customer record for the same amount. Invoices and payments (or credit notes) need to be applied to each other in order to set the Current Amount to zero and allow clearing into history.

If this is the case for you, create a cash entry for the customer and select all the invoices and payments that net to zero. Make sure that the total amount for the entry is zero. Then you can post this entry and later on, they can be cleared to history.