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That is some odd behaviour! So when you go to restart there is no spark being generated, no fuel pump or just nothing happening at all? I doubt they have thermal protection on the board (there is meant to be a cooling duct that runs across the top of your PAS pump pulley into the ECU box, so make sure thats there), so could be a case of sticking a fresh board in there. IF it was wiring I would reckon it would do it all the time/random/over bumps rather than just when its hot
Mine seems to make the ECU cut out when the engine is idling, and not restart for 10 minutes or so.
This only happens when it's got really hot - stop/start traffic on a hot day.
I reckon it's going to be some wiring, or a relay, which has suffered during the 20 years it has been in existence. Just need to find it, but that's the challenge.