DSL504 router intermittent disconnection problem was resolved by hooking it up to a UPS (uniterrupted power supply with good voltage and frequency stability).
That solved the problem. Take it off the UPS and the dang thing needs a manual reboot or a software reconnect about twice a day.
It's just another one of life's little irritations. I'm not sure whether something simpler than a battery-driven UPS might be out there on the market (that's capable of purifying the power).