IPHONE 4S factory unlocked turns off and wont turn back on.

I had this problem a week ago. I had 20% battery left, walked away, was expecting an important call.. and an hour went by. I thought no way did it die in an hour on standby. Picked up phone. BLACK SCREEN. I pressed the power button, nothing. I thought, hmm guess it did die. I plugged it in, waiting about 10 minutes for the charge display to come on. NOTHING. I tried to power on again. NOTHING.

I log on my computer to find SEVERAL POSTS on SEVERAL forums about this issue. I reset with the home button, and it turned on. I missed an important call because of this, so I did a restore. (as suggested by apple's support page about the issue) BUT

Tonight, same thing, battery was still charged, phone was in a nice temperature controlled room, not in a case, and safe on a desk. Nobody was home. I went to check my email. DEAD AGAIN.

Obviously this is a quirk with this phone. I've seen so many complaints, and people exchanging phones with apple, only to get a new phone that does the same thing. What is the issue? Is it known and documented? Or will the blame be placed on the consumer spending enough money for a mortgage payment to buy one of these things?

ALSO - I want a replacemement phone. Does the phone record such crashes and would a genius be able to figure it out and explain why or at least see that it happened so I dont waste a 2 hour drive to an apple store for nothing? I honestly want a replacement. I'm afraid if I go to sell the phone in a year to get the newer version, that I'll be labeled a fraud because the phone keeps dying. I'm only 2 months into my 1 year warrantee.

THANKS!!

iOS up to date and has been.

Iphone 4s 32gb

purchased brand new from ATT

They unlocked it and I use tmobile sim.

(people that use supported carriers have the same issue, so do not throw my mobile provider preference in my face and say "it's not supported". PLEASE. I'm locked in a lengthy contract - should I be punished and not be able to have an iphone? No.