Check if you have certain apps installed such as: Battery saver-app, Task manager, Task killer-app, Anti-Virus-app.
Uninstall those apps and see if the problem is solved
If problem persists you can try to do a repair of the phone software?
Click on this link to get Sony PC companion:
http://www.sonymobile.com/gb/tools/pc-companion/
Start PC companion, start "Support Zone", start "Update phone software" and click on "Repair".
Follow the on-screen instructions.
