iPhone will not turn off.

My iPhone will not turn off. I did a restore about a week ago to repair the problem following which the phone would turn off albeit with some difficulty: I had to hold the top button down and not merely click it before the phone turned off but not so long that I would get the shut-down screen.

Now, however, even after doing another restore, the iPhone will simply not turn off, no matter how long I hold down the top button. Nor do I ever get the shut-down screen. I've had to turn on the auto-lock option so that while I'm carrying the phone around it does not randomly dial or go online.

I'm guessing this might be a hardware failure but wanted to check first to see if anyone else has run into this problem.