This really did the trick for me, just now. I can shake it and twist the cable violently, but it won’t power off any more! 
Hadn’t used my Cycles quite a while because of the danger of losing everything.
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I had got the same problem with the MS, it just turned off spontaniously. I sended it back to the shop to fix it and since then i got no problems anymore. Think it was a connection inside the machine.
…yep, that power socket end on the machine turns quite into an angle once plugged in, easy to hit a few times without really noticing…and then it gets a little loose…and the machine starts to shut off randomly…it’s usually never the power supply itself…just that end connector…