Hard to say what's causing the problem. I suggest that you turn off the phone by press and hold the power button and volume up until the phone vibrates. Then start it as normal again.
If the problem persist, you can try to repair the phone software using PC Companion:
http://www.sonymobile.com/update
In PC Companion, press start on Support Zone > Start on Update the phones software > Press the blue link that says "Repair phone".
If the vibration still doesn't work you should have the phone examined by a service center. Please contact your local Xperia support team for more information:
http://www.sonymobile.com/global-en/support/contact-us/
