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http://support.sonymobile.com/global-en/xperias/software/
Android version: Android 4.1 (Jelly Bean)
Latest available software: 6.2.B.1.96
Release started: 2013-08-26
The last update was released almost 2 years ago, there won't be any further updates, your phone it's more than 3 years old, it'll be wise to reinstall the latest update, if that doesn't work then the issue could be a hardware issue, perhaps you need a new battery.
If you want to flash your phone
/t5/Xperia-Z-ZL-ZR/How-to-manually-update-downgrade-root-2013-Xperias/td-p/298463
http://support.sonymobile.com/global-en/xperias/software/
Android version: Android 4.1 (Jelly Bean)
Latest available software: 6.2.B.1.96
Release started: 2013-08-26
The last update was released almost 2 years ago, there won't be any further updates, your phone it's more than 3 years old, it'll be wise to reinstall the latest update, if that doesn't work then the issue could be a hardware issue, perhaps you need a new battery.
you can repair your phone with PCC
Bridge (for Mac)
Alternatives on How to backup Xperias
http://talk.sonymobile.com/thread/36355