MBP 13 early 2011 - intermittent restarts

I bought the machine second hand in 2013. It worked fine until about a year ago (~October 2014), when the machine suddenly stopped, and then restarted. I took no action at the time, just one of those things. However in the subsequent months the problem recurred and became unacceptably frequent. The machine will now run for anything from a few seconds to a few weeks and then fail.

The fault symptoms are somewhat variable. Sometimes it appears as a kernel panic, sometimes not. Sometimes it will attempt a restart but stick with the three beeps memory warning. On two occasions it has displayed some minor video artefacts during the restart. There doesn't seem to be any recurring trigger for the failure: it can be playing music in iTunes, browsing with Firefox, pretty much anything.

I've run Apple hardware tests on it - nothing found.

The machine is only using standard software, no games, nothing fancy.

When supplied, the machine had 4+4G of memory and a 320G hard disk. As part of eliminating possible causes I changed the HD for a 500G version, and replaced the memory three times (using Crucial memory sticks). I completely wiped the HD, did a clean install of Yosemite, and reinstalled all the programs from originals; I transferred only the data from the old contents.

The machine has been to the Genius Bar something like six times. The first time they recognised the symptoms and said it was the hard disk cable. This was replaced and the machine worked fine. For a couple of months. There were a couple of occasions when the Genius Bar said that as the machine hadn't failed while they had it there was nothing they could do - which was not unreasonable, intermittent faults are tricky!

Then the Genius Bar replaced the motherboard. Again the machine worked fine, for a while, but then it was back to the same behaviour - although the symptoms had changed slightly.

For the last six months or so I have been saving copies of the console log and error reports (when generated), in order to help (I hope) the Genius Bar when I go next time, planned for the end of November. There's nothing glaringly obvious to me that gives any clues as the cause of the failures, the failing processes seem to be arbitrary. That said, I'm no expert when it comes to interpreting error reports.

At the moment my best guess is that the second mother board was / is also faulty. The chances of that happening must be pretty small but what else is there?

I'd be grateful if someone can help me "think different" about the problem!

Thanks

Keith