http://www.fiatspider.com/f08/viewtopic.php?f=5&t=22833
The consensus was generally that voltage drop in the ignition switch could be the cause. I had tinkered with stuff and the problem has not happened since. However I resolved to put a pair of ignition relays in to make sure it never came back, and to reduce the potential for issues with the ignition switch. This is how I did it.
First I laid out a design and wrote myself some step by step instructions (if you go to the flickr page - link below the picture - you can see it in higher resolution).

http://www.flickr.com/photos/60643179@N ... otostream/
I had another design that moved the starter current off the switch as well, but ultimately didn't do that, largely because 3 relays on a plate were too large to fit anywhere convenient.
I looked around for the highest current relays I could find, and eventually settled on these
http://www.waytekwire.com/item/75302/HI ... RELAY-12V/
They are 50 amp relays, which may be a little overkill - but I wanted to be sure that they would handle any load I put on them. I also did not use the connectors, but used crimp connect fast-ons directly onto the terminals. This is because the sockets are generally not rated for 50 amps and all the ones I could find had light AWG wire.
That nicely laid out design went largely out the window when I actually got under my dash. It turns out that my wiring was pretty butchered (so it was more important that I do it than I would have thought). Here's the wiring on the back of my switch.

You can see it is melted and butchered. The PO soldered some of the wires. What you can't see are the fact that he deleted the ignition switch connector and replaced it with individual fast-on connectors (which probably made the job easier), and he rewired the switch. Normally the brown wire goes to 30 and drives the red (starter) and blue wires. The black wire goes to 30/1 and drives the pink wires. This splits the load across two sets of contacts on the switch. In my car he had moved the black wire to the other 30 connector (so black and brown were shorted together) and he had moved the 15/54 output to 16 so basically all the power in the car was routed through a single set of contacts in the switch.
I had previously put in a set of headlight relays - so that's probably the only thing that kept the switch alive.
I mounted the two relays to a plate:

And mounted the plate under the dash right over the fuse box. there is a dash mounting screw there that I could use to hold it in place.

I moved slowly and carefully - and had to deal with a lot of hacked up wiring, so it took me an afternoon. With clean wiring it would probably be a couple of hour task. I also pulled the ignition switch, which made accessing the wires much easier.
The car runs ... although the brake lights don't work - something to debug tomorrow. I probably knocked a connector loose when I was under the dash.