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Do you have a protective case or anything covering the proximity sensor?
Test your phone with this
https://play.google.com/store/apps/details?id=com.sonymobile.androidapp.functiontester
you can also re-install the software
Update Service (SUS)
http://www.sonymobile.com/gb/tools/update-service/
http://www-support-downloads.sonymobile.com/Software%20Downloads/Update_Service_Setup-2.11.12.5.exe
Bridge (for Mac)
Alternatives on How to backup Xperias
http://talk.sonymobile.com/thread/36355
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Anytime 
I have this very same issue, not a major deal but annoying, I have run the proximity test which didn't pass.. Does the phone need replacing or is there something i can do.
Regarding the proximity sensor:
If you close the flap at any time, the screen should go off, atleast till the flap is closed, and then come back on if it is opened. If not opened within you set sleep time, then it should sleep. However, this is not what happens on the xperia, which is quite strange in this advanced smartphone world. S4 does exactly what i'm talking about.
I haven't checked this on the S4, are you saying that the S4 has a sensor per flap?