Note: If you open the context menu over a recurring  appointment and select "Edit Appointment", when the EditAppointmentDialogis shown, the EditRecurrenceDialog is shown as well. But when the EditAppointmentDialog is shown by double clicking, the EditRecurrenceDialog  is not opened at all.

Workaround:
 this.radScheduler1.SchedulerInputBehavior = new CustomBehavior(this.radScheduler1);

public class CustomBehavior : SchedulerInputBehavior
{ 
    public CustomBehavior(RadScheduler scheduler) : base(scheduler)
    {
    }

    public override bool HandleAppointmentElementDoubleClick(object sender, EventArgs args)
    {
        MouseEventArgs mouseArgs = args as MouseEventArgs;
        if (mouseArgs == null || mouseArgs.Button != MouseButtons.Left)
        {
            return false;
        }
        FieldInfo fi = typeof(SchedulerInputBehavior).GetField("beginEditTimer", BindingFlags.NonPublic| BindingFlags.Instance);
        Timer beginEditTimer = fi.GetValue(this) as Timer;
        beginEditTimer.Stop();

        if (!this.Scheduler.ReadOnly && sender is AppointmentElement)
        {
            AppointmentElement app = sender as AppointmentElement; 
            this.Scheduler.ShowAppointmentEditDialog(app.Appointment, app.Appointment.MasterEvent != null);
        }

        return false;
    }
}