Iphone 6 keeps turning on and off

Try Some Troubleshooting?

1. Restart:  Press On/Off button until the Slide to Power Off slider appears, select Slide to Power Off and, after It shuts down, press the On/Off button until the Apple logo appears.
2. Reset:  Press the Home and On/Off buttons at the same time and hold them until the Apple logo appears (about 10-15 seconds).
3. Restore:  Connect your iPhone to iTunes on your computer, backup, and then select Restore to Factory. If you forgot the passcode for your iPhone, iPad, or iPod touch, or your device is disabled - Apple.

For help with the above on later models including iPhone 7, 7s, 8 or later, iPad Pro 11" and iPad Pro 12.9" models please refer to If your iPhone, iPad, or iPod touch won't turn on or is frozen.

If all else fails then make an appointment at the Apple Genius Bar for service. If you need to find an Apple Store - Find a Store - Apple. If you did not purchase it from Apple then you will need to look to the vendor for service or How to find your nearest Apple Authorized Service Provider (AASP) or Distributor (AAD).

Frankly, I would remove the Norton software entirely. It really isn't needed. if you want VPN protection then purchase it independently from one of the hundreds of providers. The software is usually free but the service is charged by month or by year (your choice.) Personally, I use TorGuard which I can recommend.