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Try running it in safe mode for a while and check if you still experience any shut downs.
http://talk.sonymobile.com/t5/FAQ/How-to-boot-your-phone-into-safe-mode/m-p/348008#U348008
If you do and you have tried to reinstall the phone software via SUS you should contact your local support team to have this examined at a repair center.
http://www.sonymobile.com/global-en/support/contact-us/contact-info/
Thanks but it didn't work, phoned up Sony its getting sent away for repair a bit gutted but hopefully quicker the better. Has their been a issue with the z1 overal ?
I had 3 Xperia ZLs and they all had this problem in common! From my research, seems to me all the sony series do this! And all the carrier tells me is to repair or replace, which I repaired one and replaced two. Very very frustrated at Sony about this!! It`s like I'm stuck in a loophole!!!