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Have you removed the SIM to see if the same occurs?
Yep, had this a few times... I actually had it last night; was taping away posting something on another forum, quick pause for thought, screen went black as if to sleep but then wouldn't wake when I pressed the power button! Ended up having to hold the power button just to restart the phone.
I'm really hoping that Lollipop will be the end to all this little niggles we seem to be having but I fear it'll just open up a whole new can of worms 
I've nearly had this phone a year now and although I love it (just!) I still think it's only about 75% as functional as it could be.
It'll be wise to repair your phone with PCC
Bridge (for Mac)
Alternatives on How to backup Xperias
http://talk.sonymobile.com/thread/36355
I would love to do that but I was under the impression that if I did I would lose everything. I can't afford to do that at the moment so I'm having to just put up with it...
Coming from an iPhone I would like to be able to do a full backup, update/restore and then restore my backup to my phone. Then be able to use my phone straight away with no reconfiguration, manual adjustments etc. By all accounts this isn't possible with Android, yet.