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If a hard reset does not help, then try a backup followed by a factory reset. Before restoring from backup, check to see if the phone will keep you logged in (this rules out any 3rd party apps causing the issue). If that still does not work I recommend taking the phone in to the Apple store and letting them help you.
To hard reset (this does not delete anything from the phone); Press and hold both Power and Home buttons at the same time until you see the Apple logo. Then release both buttons and allow the phone to reboot.