In Sword Art Online after the episode "The Black Swordsman", Kirito does not get any HP back during his fights with Heathcliff.
What happened to Kirito's healing?
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Sign up to join this communityIt's a fairly small amount of healing compared to his overall health-bar. If we go back to the episode where he talks about his "Battle Healing" skill (Episode 4), Kirito states that he has 14,500 HP, and that his skill regenerates 600 HP every 10 seconds. That's 4% every 10 second tick, but most attacks we actually see players take from similarly leveled enemies do WAY more damage than 4%.
Practically speaking, the skill is mostly for getting rid of accumulated minor damage, either from status effects (weak poisons), trash mobs or other damage-over-time (DOT) attacks, so a player doesn't die from a thousand stings. Passive healing like this in MMOs tends to be fairly weak like this, mostly serving to save you some health potions, and in fact this skill is basically oriented towards solo players, because they wouldn't be able to take healing potions mid-fight (as they have to be manually drunk), unlike players with party members you can switch with. The downside of course is that SAO has a limited number of skill slots (expanded on more in the Light Novels, especially SAO Progressive), so most (non-solo) players likely woulda just settled for using some weak potions HOT (heal-over-time) once in a while, and saved the skill slot for something useful.
As it so happened, in Episode 4 Kirito was visiting the lower floors, and as such the players that attacked him were all low-to-mid level players that were basically trash mobs that Kirito simply out-leveled by a wide margin—and trash mobs are one of the exact sorts of things the skill was meant to counter.
On the other hand, other players that were of similar level, like Asuna, Klein, and of course Heathcliff, would barely notice the passive healing unless he could avoid enough hits long enough for it to make a difference.
Two possible reasons:
It was simply overlooked. The fact that the battle was happening at all was probably more germane to the immediate circumstances than whatever abilities either player had.
It was probably underpowered compared to the DPS that Heathcliff could dish out, which is fairly common for MMOs to have an ability either become eclipsed by another one or made obsolete due to the people/NPCs being fought. If it healed something like a value equal to the skill's level every 10 seconds, and Heathcliff exceeded that damage ratio, then suffice to say it wouldn't factor into the fight.