More precisely, everything seemed fine until the lights came back on. We had a brief power outage last night. Not too long, but long enough for me to decide to shut everything down before we ran out of battery. On restart one of my web servers just could not get traffic past the cable modem. Now, I know that Cox has limited the number of MAC addresses the modem will service. What I didn't think of was that the "intelligent" Cisco switch was going to effectively claim one of those slots by spitting out all of the management traffic that it does (Spanning Tree BPDUs, CDP, and perhaps IGMP snooping, etc).
In the end I wound up dropping my Internet connections back into one of the "dumb" Netgear devices. Problem solved. Next up (in my burdensomly copious free time) I will probably poke at that Cat to see if I can get it to shut up entirely on the ports configured for Internet use. A "no cdp enable" and "no spanning tree" directive per port will probably fix it...