The recently updated calendar is key. As are having fresh prices, like @Evelyn mentioned.
Two ways to easily and automatically ensure you have a calendar updated daily:
1) Connect a .ics calendar, like a Google Calendar. Even if you don't block off any dates for bookings, Airbnb will still sync with it at least daily and that will show you have an up-to-date calendar
2) Use a pricing service (like Beyond Pricing) or calendar service (like BookingSync), which will sync prices and/or availability every day automatically. It's a nice bonus!