I can't immediately tell when overdue invoices had a reminder sent.
How about a new setting "Remind again after" which would be the number of days after a reminder that an invoice needs to be reminded again.

As an example, set the Remind-again-after to 7.
When a reminder is sent, invoice moves to new category "Reminded".
After 7 days it reverts to Overdue again.
Then all we need to do is send reminders to Overdue.