I was seen this happen a few times, and its a bit of a slow process, because a lot can cause this...
First, check and see if you have any application management apps downloaded (task killers, task managers, etc), battery "saver" apps, or any memory clearing apps. Get rid of those. There are others that glitch and can cause power cycling, but they are hard to list. Wait and see if the issue persists.
The step we want to take next is to power off the phone and remove the battery (hard reset). Wait about 30 seconds and put it back in (ensure the battery is connecting properly), making sure the battery cover is completely secure again. That battery cover can cause signal issues and shorts if not connecting properly.
Wait for about 100 hours. If the issue persists, back up all of your data (SD Card files *should* be safe), and go into Settings -> SD Card and Phone Storage -> Factory Data Reset ***THIS WILL WIPE YOUR PHONE!!!***
After that, go through the initial set-up, making sure you have your Google account log in ready. All your apps will re-download, contacts will be restored from their backup location (Backup Assistant, Google, Facebook, etc).
The only things you really "lose" is SMS messages and homescreen configurations, which you can backup SMS by downloading, you guessed it, an SMS Backup app.
If this does not work, call VZW Tech at 800-922-0204, explain to them you removed any potential harmful apps, did a hard reset, then a factory data reset, and your phone still power cycles. The Tech rep may be lost at first, because he will have to think if there is anything else but to replace the phone, which there is not. Be gentle and laugh with them. We will get you a replacement that does not power cycle.
Facebook
Twitter
Instagram