The tech suggested that if it happened again that I should try running the connection directly to the computer, cutting the router out of the equation. I fooled around with that last night, but it had no effect. I checked for viruses and spyware, but the machine was clean. The same thing was happening to the other machine on the network, so I was pretty sure that it wasn't either of those, anyway. I also finally reinstalled Zone Alarm, just to see whether someone was banging away at my ports, and if those break-in attempts were disrupting things. There were about 90 attempted pings and UDP probes overnight, which seemed a lot to me, and I was able to correlate a couple of disruptions to specific UDP probes, so maybe that's it. Bother.
Going to have dinner with Tom and Betsy tonight, so I probably won't have a chance to look at it further until tomorrow.