Thanks all for the suggestions. I've replaced the GFI outlet already,
so I'm pretty sure that's not the culprit. I'll pull all the affected
outlets and see what I can see in terms of loose connections.

The house was built in 1994 or so and there are several circuits
protected by GFCI. There have been situations in the past where the
upstairs bathroom has gone dead, and resetting the box in the
downstairs bathroom was always the cure. There is definitely something
wonky going on in this path.

- David