Sounds like either a self-resetting breaker is blowing then resetting,
or a cable (perhaps a ground?) Has broken in such a way that when it
gets hot, the break opens up, and when it cools back down, the break
closes again.

I think I have a manual that will cover the schematics of this year, and
will
see if I can find anything unusual about it.

The earlier passkey systems usually worked only when you were trying to
start the car, not after it was already running.  (I just defeated my system
on
the 90 Reatta because it was so touchy.) I'll see what changes were made to
the later systems.

I have had a bad ignition switch on a Ford behave similarly, not the key or
the
cylinder, but the switch itself.

Will get back with you.

I did a quick schematic check, Libby.
The radio memory runs from a line that should be hot at all times. It
does not go through a switch or relay, etc.  (So forget the ignition switch
idea).

To totally lose power, intermittently, I would look at

(1) battery cable....again... The Buick battery cables are often multiple
side mount
units.  They can become corroded inside the rubber covering, and this is a
common
mode of failure.  The rubber can be pulled back and the internals can be
cleaned
but this may provide only temporary relief.  For example, the cable to the
starter
may work okay, while the other may not be getting current due to corrosion.

(2) I suppose the battery itself could have an intermittent cracked plate.
Not too
usual, but it has happened.

There are other places where intermittent contacts can result in this sort
of behavior.
Maybe the other regulars know some of the weaknesses.