Ok here it is, when I updated my 3GS to iOS 6 there are times that my iPhone is freezing (when I used the "Tap to Tweet" button) and my iPhone just auto restarting for a couple of seconds. Is this auto restart thing is a new feature of iOS 6 or just a bug?
It may be an odd bug or a hardware failure or a sign that the OS didn't install correctly on your device.
You could look at the logs on the device or go through some of the troubleshooting steps to see if you need service or just to try restoring the OS again.
I would send in the diagnostics and work through the steps listed. Alternatively, if your phone works for several minutes, you could also browse the error logs from Settings > General > About > Diagnostics & Usage > Diagnostics & Usage Data
Look for LatestCrash and panic entries first - and then perhaps other log files might be of use. These logs also can be synced to a computer for easier searching with iTunes, Xcode and other programs that read files from iOS devices.
This problem might be you have an old iPhone. The first version of the iOS for iPhone 3GS is 3. I think you should downgrade.