This is not normal, but it happens on occaision for me. Try hiting the little reset button on the back with a pen, that fixes it for me. I've had this happen about 5 times in about 8 months.
I have a similar issue (easily fixed though). Sometimes when I turn my controller on, only the analog sticks function, the d-pad and Cross, Circle, Triangle and Square don't respond, but one press of the TacSwitch and everything is normal. Very minor and mostly negligible.