Invoices typically are marked as paid when you receive another customer payment.
For as long as the prepaid money lasts, you should once in a while record a new customer payment in the amount of $0.00 and Apply existing credits towards Outstanding Invoices:
The $0.00 payment transaction, when saved, may not result in a register transaction, but it will make updates to take the prepaid amount into consideration when marking invoices as paid in full or part.