Powering up/down issue

This only happens every so often (about once every two weeks or so) but when I power up the iPad (I power up in the morning and power down overnight), instead of the Apple logo, I get the spinning cogwheel usually displayed when shutting down and then the iPad does, indeed, power down. I have to push the power button again to get the Apple logo and begin the normal power-up sequence.

In observing this behavior, I've noted that when I've powered off the iPad and the cogwheel spins for longer than normal (it usually only turns once or twice before the iPad shuts off), this usually indicates that I will get the "powering down" error on startup. It's almost as if the iPad didn't finish shutting down.

Again, this only happens once every couple of weeks or so - it's by no means chronic - but I was wondering if anyone else has seen this behavior? I'd bring it to the Genius Bar but it happens so infrequently that the odds of it exhibiting this quirk while I'm there is slim to none.

I'm starting to wonder if it could be a misbehaving app...