I have an iphone 4 (running 6.0.1) that will shutoff if left idle after locking it. If I push the power button (top right) to lock the phone I can push the home button to bring it back up as long as I push the home button within 25 or so seconds. If I wait longer than that the phone shuts off and the only way for me to turn it back on is to hold both the power button and home button together.
I switch the auto lock to never and let the battery run completly dead then charged it back to full with no interuptions. I have also reset the phone.