I have same problem. I was brought it to sony service center, after 5 days checking, customer services said that my phone's power button and LCD need to replaced. I was suprised. Why the LCD must be replaced too? And then I was waiting for about 5 weeks of repairation, my phone's button is back to normal but not so long, just for 3 weeks.
I've try to using apps like proximity action and smart screen on/off -> not working
Factory reset -> not working
Try this solution offer ([post|140748]) -> still not working