My Kenmore HE3t has more stringent balance criteria for the high and extra high spin speeds than it does for lower speeds. Although it doesn't happen very often, if it is having a hard time properly balancing a load, I change the spin speed to medium and let it spin a minute or two. I then pause the cycle and switch it to a higher speed. It does need to rebalance, but since more water has been removed from the load, it is able to achieve balance more quickly.
If it can't achieve a proper balance after many tries, it will reduce the final spin speed. I can't recall it ever aborting the final spin completely.