Rubin,
I apologize for the lack of a response, I was out of town on vacation last week.
I've looked at the script you posted and you're missing the nag interval setting. Do a compare from your script to mine and you'll see that I am logging 2 date/time stamps in the initial message and both are being checked in the alerting step. The first is checking whether or not the device has failed to check in within the threshold and the second is to determine whether or not you have already been alerted for that specific device within the last "Interval" seconds.
Also, while the all-in-one script is a more simple solution, the reason I have the other available options is because if you have a lot of devices to check and a lot of message traffic, you might not want that second part of your script to fire off 500 times/second when your threshold is set to 24 hours. If you schedule the second script to run every 24 hours, you'll get the same result without the need to go through and check every device you're monitoring every time you receive a message. Same concept with using a rule to check for keep-alives, you can set it to check the devices every 30 minutes or so instead of every time you receive a message.
I personally have devices that send messages every few seconds so the all-in-one option makes sense for me and isn't wasting any processing power that isn't needed. My lowest threshold is 30 seconds and my largest is 12 hours.
Either way, the amount of processing power is negligible and not worth fussing with unless you start experiencing performance problems, then just keep in mind, this is something you can tweak to get a few cpu cycles back.
I hope I answered all of your questions.
Acy