It seems like they have made it so we can fix it proactively, without waiting for an email from them.
I just lost my card and froze the credit card account, then added a new credit card to my Airbnb account. But then saw a message saying payment type can't be changed for an existing reservation. I then tried going into the reservation itself:
Clicked on "Your Home Reservation"
Scrolled down and under "Payment Details" clicked "Get Receipts and Manage Payments."
Scrolled down again, and under "Scheduled Payments" clicked "Update payment details."
It then gave me the ability to select the new card and click "Submit."
There was also the option to pay the second payment as scheduled in a few days, or to pay now. So to test if the new card would work I chose the “pay now” option.
A few minutes later I received a receipt via email saying that the balance had been successfully paid by a card with the last 4 digits of the new credit card.