Around 3 times during the last 3 or so months, I have gotten in my car
to find the clock and radio had lost their settings, as though the power
had been off. It happened once overnight with the car in my garage and
once during the day with the car parked outside at work.

It happened two more times within the last few days, but in these two
cases everything seemed fine until I hit the starter, then total power
failure.

When it happened today, I popped the hood latch and got out of the car
to just have a look, with the ignition turned on. When I closed the door
after getting out, the vibration of the door closing turned everything
back on... I started the car and drove to work.

Battery posts and terminals are pristine and tight, so it is apparently
somewhere else.

Are there any known problem spots like this for older Hondas? The car
has about 70K miles on it, but of course is older in years than miles. :-)