It does slowly cycle the brightness, but that's normal. Are you saying sometimes you plug it in and the light doesn't come on at all? If so, what about the on screen indicator? And does the screen itself even turn on automatically when plugged in?
If none of that is happening, then it's not charging. The usual culprit is the USB cable going bad. It's also possibly a bad USB port or charger, but those are much more rare.