No problem here! Fons can create an appointment up to 72 hours in the past for cases like this. The billing cycle will begin from whatever the actual day is, but once your client confirms their appointment "in the past" the Fons system can be set to recur each week or each month, thus saving your client and you from having this issue again.
For clients under "per appointment" billing, you can manually override your next appointment's rate to add the missed charge.
Last, but not least you can also send a "One-Time Payment Request" to send a single invoice to your clients to account for any missed appointments.