Question about the H-mechanic

This might be obvious and I'm just not seeing it, but...

how exactly is the H-mechanic handled in case heroes are flipped to their incapacitated side?

We had a game vs. Ennead, where we lost Mr. Fixer (untimely death due to Bloody Knuckles, but he sure did some damage ; ), then Bunker went down and all we had left was Promo Fanatic. 

We then figured, since only 1 Hero Character was alive and had a physical presence on the battlefield (Atlantis), that our H went down from 3 to 1, leading to a close victory, with Fanatic dealing out some mean damage and never dying cause of Fixers and Bunkers incapacitated powers combined with her relics and abilities.

However, I am not sure if we would still have made it without being able to "circumvent" quite a few of the Enneads damaging cards, with H at 1 leading to 0 damage.

So the question is, does H stay the same throughout a game, even with Heroes dying and furthermore, in, for example a 2 Hero game, should H be still 3, in order not to break the game mechanics or something like that? (Villains and Environment would still have their turns more often, compared to a 3+ Heroes game, so still a higher difficulty I think)

H is the number of heroes who started the game. It does not change if you get any incapacitated.

The H stays constant throughout the game ...

A hero still offers his/her Incapacitated Ability, even when incapacitated.

As mentioned, H is always the number of heroes who started the game - they're still present even if incapacitated. However, if anything affects active heroes, then you can ignore incapacitated ones, because they're defeated and no longer properly "active".

So basically the Enneads defeat was unjustified and they are right screaming for revenge...

Thanks for the clarifications!