This person had issue with their router loosing sync and requiring a reboot periodically, so they made a power switch that pings Google every 5 minutes and that power cycles the modem (with a 30 second down time) if it can't reach Google. (link)

Pretty ingenious, although, although, I don't remember the last time I've had to reboot my router. My guess is there's something wrong with the router or the copper lines (if they're on old ADSL).