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There could be anumber of reasons why your handset would shutdown. If you can open the .plist file(You will need a mac) then it may give some clues as to what is going on.
Intersm of a replacement phone there is two options.
Going directly to apple would be your quickest option however would require you to travel to the apple store
Thank you for your posts and there has been some fantastic suggestions already from Nabs (thank you).
Just to add to that please could you also try the option of performing a full back up using iTunes and performing a full restore of the device and let us know how you get on.
Thank you for your post and I am sorry to see you are still experiencing difficulties.
It certainly sounds like a software issue, please take the device to your local store and one of our experts will be able to take a look and advise you of your best options or alternatively we can arrange a postal repair.
Please can you ensure that all of your contents and information are backed up.