Over the weekend I was at a friend's house and he was rough housing with our two three-year-old boys. My friend weighs about 250 lbs. Each boy, less than 40. My friend could easily ignore one while picking up and throwing the other onto a nearby couch.
Now...I know what you are saying...rough housing isn't fighting. Give the two kids knives, make them know how to use them and have them going for the groin, behind the knees, etc and then let him ignore one of them...
Okay...make him a Balor with a DR of 30/+3 and our two "halfling rougues" completely unable to harm him(even on a crit). There are times in D&D when an opponent simply cannot damage you(or distract you in any reasonable way).
If I wanted to introduce an ignoring rule:
On your turn, you may declare that you are ignoring attacks from one or more particular foes. This gives the following benefits and penalties:
1) An ignored foe cannot be counted by allies for gaining flanking bonuses or any other similar advantage.
2) An ignored foe is effectively invisible when he attacks you.
3) All hits by an ignored foe are critical threats.
4) If an ignored foe does even 1 hp of damage to you, you no longer are ignoring him and you cannot ignore him again until you've taken 2 turns.
Why 3? Because if your foe really cannot hurt you, then even crits should not hurt you...otherwise, you best not ignore him.
That said...I wouldn't use such a rule...I only use house rules if I deem them necessary to keeping the game fun(or will make the game significantly more fun). This is no more necessary for keeping the game fun than a more realistic hp model, IMO.
Edit: Oh....And I know what IceBear is saying: Then why don't invisible characters automatically critical threat on every hit? The difference is that an attack is more than a single swing of a sword. Presumably, as soon as an invisible attacker makes his first move, the defender begins to twist/dodge/duck/etc. to avoid being hit by the unseen foe.