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Unfortunately, I find it no way to free up the date in the Date Reservation Widget when someone cancelled their reservation. A workaround for now would be to add our widget like Appointment Widget (http://widgets.jotform.com/widget/appointment_slots) and add the free dates there. You can label it as "Free Dates from Reservation" so clients can distinguish that.
I have also forwarded this thread to our developers as a feature request. We can't promise any timeframe for this, but if there are updates, you should know it via this thread.