Fortunately nothing "just happens". I figure there must be a firmware error, or something like that. My assumption is that Sonic pushes out such things periodically, though I have not kept track of versions over the years and I don't really know how old the currently installed version is.
The modem model is 4111N-030 Hardware version 2701-000816-003 Software version 22.214.171.124.8. I've been using it for just over 4 years.
Just now I checked again and I find that on this computer DNS is no longer set to the modem itself. Instead It has reverted to the defaults, Sonics own two server addresses. The settings on the modem are still the ones that I put in, namely 126.96.36.199 and 188.8.131.52.
Please correct me if I'm wrong, but I think I should be able to reset the DNS settings and have the DHCP server either use whatever settings I've set it to or complain if there's some problem, not silently use other settings.