@Oshi0 If you go to Your Reservations/ Reservation History you do not get the option Send or Request Money for reservations that have been cancelled; you only get it for reservations that have not been cancelled.
@David1023 The reason you couldn't refund money to your guests was because they cancelled, not because their reservation is in the past.
One point to note: if you use the Resolution Centre to refund money, the money is taken off your next booking. (I refunded a guest from overseas who double-booked me with another room on another site. She rang me in tears and I took pity and refunded her. This was at the end of the season and when I got my next guest's payment after a long gap, I initially couldn't work out why the payment was wrong.)
You can offer free accommodation in the future to your guest, or search Gift Card in Airbnb Help. These are available for use in the US at the moment.