Select Make recurring in an invoice's More menu, choose how often and the date of the first invoice, and optionally how many to send. Magpie issues and emails a new invoice with the same lines on each date.
Recurring in Invoicing lists every recurring invoice. Open one to change the next date or the lines, pause it, resume it or end it. When the total changes, your client is emailed the new amount before the next invoice.
A client who saves a card is charged when each invoice is issued. If a charge is declined, the invoice is emailed with its Pay link and a link to update the card, and you are told.