Old cable modems sucked. Mine would often lock up, needing a power cycle to resume working. Very annoying when I was at work.
The quick and easy solution is to monitor the connection status and flip a relay to reboot the modem. But how to monitor the connection? Setting a single host or IP seemed like a bad idea because it would have added an extra, and totally unnecessary, single point of failure.
Instead, my home router (slackware box with 2 ethernet cards) collects the IPs that I connect to (by watching the conntrack stuff in /proc/ ), and if it can ping them, adds them to the ping list. It then pings random selections from that list to verify connectivity. IPs are removed if they are unreachable for a while (until it decides the connection is down; no point purging the whole list because of an outage).
Took me a couple of hours to set up and debug, back in like 2002 or 2005 or whenever I wrote it. I presume that there is some free software to do the same task by now.
Monitoring a single fixed hostname is foolish, at best. And this is like the 3rd or 4th big story (that I can think of) about home routers acting badly because of hardcoded values.