Joe, Google does not publish when they update subscribed calendars. However, our experience has been it's often every 24 hours. Therefore, you may need to wait as much as 24 hours to see your Elexio Database changes reflected in Google Calendar. You can delete/re-add the calendar, that doesn't solve the problem as Google cache's the calendar URL. The only way around it is to add the calendar to a new Google account :( (I've personally set up a lot of test Google accounts to test things).
That said, if you see an event that's not been updated in over 24 hours it may be worthwhile to contact Elexio to see if they can replicate. Each calendar provider (Outlook, Google, etc.) consumes ical files slightly differently, so we have seen some unique ways Google has interpreted Elexio's ical feed, which Elexio has worked with Google to change.