After literally a couple of years of this problem I think that I have finally solved this one. (Fingers crossed!).
To be specific, the symptom is that you turn the key and there is NO ACTION from the engine. No turn over, no clicks, nothing.
For me this went from very occasional. say twice in 3 months, and recovering after 1/2 hour. to a few times a week and needing 4+ hours to recover.
Eventually I had a failure that lasted overnight, (helpfully into Saturday so I could spend time to look at it.)
I had to get right under the front of the car to be able to see the lower end of the back of the engine. This is where the starter motor is very cleverly hidden. It is a real pig to get to especially if you are over 8stone & have no ramps etc!!
Just to the left of the starter motor is a cylindrical block about 1inch dia. (Could be a solenoid or similar??) It has a single thin control wire going to it and the heavier wires for the starter motor current.
The control wire was the culprit. It has "fast-on" push-fit terminal housed in a huge plastic housing. I suspect that this is part of the problem as it makes the connector too susceptible to vibration. In addition this area is pretty exposed to muck & grim thrown up under the car so must be liable to corrosion, add in the heat from the engine and you have a horrible environment to a cheap 10cent connection. Anyway I chopped this off and fitted a new standard crimp connector and have had NO FURTHER problems for over a month.
I'm an electronics engineer, with reasonable experience on ruggedised equipment & reliability. I really would not have suspected this symptom to be explained away with a single duff connection. (Especially as it recovered each time.) However I think that this really is worth a try if you have these symptoms.
It cost less than £10, even buying the crimp tool etc. It was a really fiddlely job as there is barely enough room to get 2 hands to the wire BUT the result is that I'm now not being forced to sell the can and leave for some other punter to worry about.
(As you might have noticed I'm feeling pretty pleased with myself!!!)