I had the same thing happen to my phone about 2 weeks ago so I took it to the Apple store to see what was going on. The kid there took the phone in the back and said that it was an unfixable hardware issue and brought out a brand new phone for me. I was pretty happy about the customer service and quick replacement until the brand new phone, which I got last weekend, started doing the same thing on Tuesday, only a few days after getting it.
I am thinking that I am pretty unlucky or I am doing something wrong. I told the kid at the Apple store that I put my phone in a workout armband when I go to the gym or go for a run and asked if doing that was bad for the phone, he said that it was fine to do that. Other than that neither phone, the original working well for about 6 months and the new one for about 4 days, was subjected to any water damage or drop damage.
I just tried the alcohol cleaning of the charging port and blow drying the phone about 45 minutes ago and it did nothing. I didn't realize this was a charging port issue. I thought it was related to the headphones, because both times it started acting up was when I had headphones pluged in.
I guess I am back to the Apple store when it opens up. I really hope that they can resolve this, although I have a feeling that they will tell me they can't do anything since they already gave me a new phone. Next contract I am definitely going away from the Iphone.