I had the same experience. The error I see that pops up momentarily as it is happening was "sim card removed for protection", before I see "no sim card" or "no sim card detected". I replaced sim card twice, did all the tricks that I read (rebooting on safe mode and clearing data cache under "storage & USB", "reset settings" under "backup & reset", removing 3rd party apps that I suspected could be the cause, removing extra virus protection apps (keeping only verizon's "security & privacy". All these tricks allow my SIM card to be detected again but problem comes back a day or 2 later.
My last recourse was to do "factory data reset" but I am glad I didn't. What solved my problem was simply allowing ALL of the built-in apps to "update". I had been ignoring them because i don't use most of those apps... like google radio, google play books, google play games, etc. So, after updating all those built-in apps, not only did this problem go away, my battery lasted much much longer.