As the information that a certain event should occur at least every six hours is specific to the application writing to the log, it would be best if it could monitor itself and write a log entry if the event does not happen as it should. If the application writing log information is developed locally I would recommend this solution.
If that is not possible, I would keep the mechanism which makes sure the event has occurred as close to the application as possible. Maybe a watchdog could be started in the background from the same start script that starts the application performing logs. When the application is stopped, the script also stops the watchdog.
Another option, in case you would like to keep the start script in its original condition for some reason, would be to create a cron-job which performs the log watching.
In either case. Make sure the level of the log entry is severe enough that you are alerted to take a look at it using whatever tool you are using to monitor logs. It's better, more future proof and inclusive for things you didn't think of but should monitor, then to listen for a log level than a specific log entry. This means at least WARNING level.