I spoke with a Live Expert who informed me that this was a known problem with QBSP. His suggestion was to upgrade to QB Simple Start. This would nearly double my monthly payment from $20 to $38.
Instead, I found a workable solution on my own.
After the upgrade to QBSP, invoicing and payment have worked as expected. I send out an invoice. The bank receives a payment. In the Invoices window, I click on record payment, select the matching payment, and the invoice status changes to deposited.
The problem was only with the invoices and payments that were not matched during the upgrade.
The solution
1. In the bank transaction window, unlink the payment from the invoice with overdue status.
2. Create a new invoice by copying all of the details except the invoice number from the overdue invoice to a new replacement invoice.
3. For the replacement invoice, select record payment and choose the corresponding payment. The replacement invoice status will change to depositied.
4. Delete the original invoice with overdue status.
5. Open the replacement invoice and renumber it with the number from the overdue invoice.
6. Repeat for all overdue invoices.