If you are getting replies from clients and they are not showing up in Google Calendar. Or you have receipts turned on and they also aren't showing in Google Calendar then Appointment Reminder probably doesn't have "WRITE" access to your Google Calendar.
Login to Appointment Reminder. Go to Settings > Integration and make sure we have "WRITER" or "OWNER" access to your calendar.
In the image above you can see we only have "READER" access so won't be able to update your calendar.
Login to Google Calendar under the google account that is having issues.