Why does my phone keep turning off?

This could be a software issue, please connect to itunes and perform a backup, once baccked up proceed to do a restore, once restored set up as new phone but do not restore the backup just yet.

now disconnect from computer and test the phone to see if it is still shutting off, if not the you are good.

now connect to itunes again and restore the backup, once the backup is restored disconnect from computer again and test, if still working correctly the your all done but if the phone starts playing up again the problem will be in you backup and you will have to lose this backup by restoring and setting up as new phone again and starting afresh.

hope this helps