I purchased my first ever iPhone on October 14 and immediately started having the same problem as everyone else here. I received my replacement iPhone yesterday in a white sealed box with a paper telling how to set it up. I'm not sure if it is refurbished or not. I received it after calling Apple Care last Thursday. I have not had any problems yet with my replacement, fingers crossed. I wish I never gave up on my Droid but that's water under the bridge. As I remember though I did have to get my Droid replaced 3 times before I got one that worked properly.
When I talked with Apple Care they said they knew nothing about this problem. At first it angered me that they would "pretend to be in the dark" about such a widespread problem. I then decided to count how many people had posted on this discussion. I did a quick count and came up with only 93 people posting. If I triple that number to account for other discussions here I would only account for 300 people posting a problem. If I assume that only 1 in 100 people post a problem then we are talking about only 30,000 bad phones. Now that may seem like a lot but when Apple is selling them at a rate of a million a day, it is just a drop in the bucket. I hope Apple will find a solution to our problem soon but if we have to get them replaced time and again they will eventually get the message. All I'm trying to say here is give the Apple Care technician a break and work with them to solve your problem.