Well, this is kind of interesting. I've been using the Watchdog process described above for the past 3 days, and there's only one instance of the message not being received. Subsequent messages were received without having to repair autoremote's URL. In the past, without the watchdog, I would have had to repair the URL at least once during that time.
I wonder if the very act of sending/receiving a message every 10 minutes keeps the URL working.
I'll let the Watchdog keep running and see what happens.