I recently updated iPhone 6 to iOS 11.3. Now it keeps powering off and rebooting. I tried soft reset and also tried a total factory reset. Once all was reinstalled it was back to powering off. Not sure what to do next.
First off, welcome to the Apple Support Communities. We're happy to have you here, and I hope you enjoy your time with the forums. Secondly, I want to thank you for the troubleshooting you've done so far. Those steps you tried before reaching out here confirm what I was already suspecting might be the cause: incompatible software. Basically, whenever the general iOS environment receives a larger update (iOS 11.2 to iOS 11.3, for example), sometimes the third-party apps you use on your device need to release a newer version of their own to make everything copacetic between the app and the device.
If the restarting issue wasn't present with a clean installation of the software, and only returned once you started redownloading apps, you'll have to figure out which app might be creating the issue and forego using it until a newer, more compatible version is released. A great way to figure out which app is responsible is through another clean installation of the software. You restore the device to factory new settings again—making sure to backup your iPhone beforehand—then install a few apps at a time and test for a few days before installing more. That way, if the problem returns suddenly, you'll have narrowed it down to just a few possibilities.
It sounds like you already knew what was going on before you reached out, but I hope hearing it from someone here helps validate the idea and tells you what to do next.