I remember when I had an LG Envy, I had problems where my phone would shut off on it's own. It wasn't a big deal but my phone was crap so I wanted to use the warranty to trade it in for a new phone. I went to the verizon store and they did these things to try and fix it and told me to see how that goes. If it doesn't fix the problem, I should come back and they'll give me another phone. I went home and a few hours later, it shut off on me again. I went to the store and they gave me another Envy...but, it wasn't a brand new Envy. It was a refurbished Envy, a rather crappy refurbished one. The new phone I got was in worse condition than my original Envy. The screen was scratched and some of the keys were falling off. What I'm trying to get at is, unless the problem really REALLY bothers you, and you can't deal with it at all, you should not ask for a new phone. They will most likely give you a crappy refurbished phone instead.
Just my two cents.