I've had the exact same problem!! Bought the phone in end of April, by End of June, stopped working. Apple Store replaced the phone, worked fine for another month, same problem. Apple Store replaced the phone AGAIN in July, worked fine until one month later (August) Apple Store replaced the display this time. Worked fine for another month and now (Septmber) crapped out again!!! I am frustrated to say the least. I have had 3 new phones, and one new display in 5 months!! I take care of my phone to the point of being OCD about it, I use the OtterBox Defender case ALWAYS!! And I clean it constantly. Only thing I can think of is that I use it in my car for music plugging into auxiliary through the headphone jack, so maybe the headphone jack thinks there is still something plugged into it even when there isn't. Frustrating as !&&*, any insight would be welcomed!!
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=== Update (04/18/2016) ===
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After 4 phone replacements, and one display replacement in 6 months, I switched cases from the fully enclosed OtterBox to a Lifeproof that is sealed around the edges of the display. I am now on 7 months with no issues. Only thing I can think of is that the display was heating up too much in the OtterBox, and since the microphone for Siri and voice to text is in the display, it was frying the microphone as well. Knock on wood, I haven't had an issue since, and I was having problems every 3 or 4 weeks with every single one that the Apple Store replaced with.
I've had the exact same problem!! Bought the phone in end of April, by End of June, stopped working. Apple Store replaced the phone, worked fine for another month, same problem. Apple Store replaced the phone AGAIN in July, worked fine until one month later (August) Apple Store replaced the display this time. Worked fine for another month and now (Septmber) crapped out again!!! I am frustrated to say the least. I have had 3 new phones, and one new display in 5 months!! I take care of my phone to the point of being OCD about it, I use the OtterBox Defender case ALWAYS!! And I clean it constantly. Only thing I can think of is that I use it in my car for music plugging into auxiliary through the headphone jack, so maybe the headphone jack thinks there is still something plugged into it even when there isn't. Frustrating as !&&*, any insight would be welcomed!!