Maybe the display cable have flex and loses connection.
I think you need to bring to your local Sony Xperia for inspection.But first contact your local Xperia Team
Try the suggestion by @Jake-SonyXperiaSupport
If you still face it,then you might have a defective LCD.And the best way to overcome it is by contacting your local Sony Xperia.
http://support.sonymobile.com/global-en/contactUs/