I'm having the exact same issue.
Mine's been acting up for a few months now. I don't know why, but for some reason, like the OP, there are times where I press it many, many times and it just doesn't work. Other times, it will just work again. I should also add that this happens at random.
I've sent it in to Apple ****ing twice, and I'm getting pretty fed up with them not being able to reproduce the damn problem. I know I can repair it myself, but seeing as to how I have until August 6th until the warranty expires, I wanna see if I can get a replacement phone. This is ****ing driving me nuts that they can't seem to replace it. :|
And right now, an Apple Store is a no go, since I won't be near one until the 25th, and by the time I get to it, the warranty is going to be expired.
I'm at the end of my rope, because if I've called Apple twice about this issue, it's obvious that this hasn't been resolved.