random shutdown iphone 4s

Try This...

Close All Open Apps... Perform a Reset... Try again...

Reset ( No Data will be Lost )

Press and hold the Sleep/Wake button and the Home button at the same time for at least ten seconds, until the Apple logo appears. Release the Buttons.

http://support.apple.com/kb/ht1430

Next...

Connect to iTunes on the computer you usually Sync with and “ Restore “...

http://support.apple.com/kb/HT1414

If necessary Restore as New...

If you try all these steps and you still have issues... Then a Visit to an Apple Store or AASP (Authorized Apple Service Provider) is the Next Step...

Also consider Deleting any Apps you have Purchased / Downloaded but you now never use..

I have the same issue, but as I'm also out of warranty, Apple want £150 to repair.

Mine seemed to be worse in the winter, shutting down even though I would have 40% or 50% battery left.

A few minutes later I would be able to turn it on ok.