Phone shutting off and having trouble getting LTE

So this is my second iPhone 5s. The first one after a couple months decided to completely drop my service, making it impossible to connect to LTE and only going up to 1 bar and then dropping back down to no service. I called in and they sent me a ne phone.

Now I am having pretty much the same issue except now my phone is turning off randomly, in the course of 8 hours it has done it 6 times and counting. My service is fluctuating between 3G, 1 bar, and occasionally LTE, abd mind you I'm in a place where I ALWAYS have perfect service. I have done all the things that need to be done in order to fix the issue, turned the phone on and off, held down the home button and lock button, reset the network settings, etc. etc. etc.

Nothing has worked, so before I contact apple and attempt to have them send me another phone, has anyone else been having the same issues that I have and if so what is the trick to fixing this, its quite inconvenient.