I noticed that with me, I would grab it in the same spot as before and had perfect balance, but when the weight went up, it would lean one way or the other. A lot of that has to do with your grip failing. Obviously we're not perfectly even in regards to grip strength and which fingers have more power. Personally, I just move my grip a little bit back since my ring and pink fingers are losing the grip sooner (they actually extend out from the bar a bit) which leaves the mid point of the bar in between my pointer and middle finger instead of right at my middle finger. This way, if my pinky/ring fingers start to lose grip, the bar doesn't sink backwards.
Does that make sense? It's easier to show in person than put it into words I guess.