Nope, they live like champs.

Insert Obligatory "Holy Grail" reference here.

The problem, as Altar clearly demonstrate, is that the AI has no clue how to keep it's henchmen alive (they need to be babied). As a result, if you make them die, Altar gets pretty crippled by its special units (it would just be a massive influence drain for them). This is the same logic behind perma death for champions.

I had a warrior that was blind in one eye and close to -50% hp, he was pretty fucking worthless after 4 injuries.  Although most of my injuries happen in the early game where I am gambling a lot more and fighting a lot of one champ vs monster battles.  

henchmen are really thoroughly overpowered. However i don't think taking away their immortality would be a good way to weaken them .it just wouldn't be fun  The immortality of champions is a means to discourage save scumming. It's really annoying to constantly reload to avoid losing your favourite pet lv30 unit. it sucks fun out of the game. Letting them live, but with an injury, is a way to penalize death that players can shrug and accept, compared to the permanance of death which is just annoying.

The main issue with them is that auras like shieldwall, tactician and trainer seem to stack infinitely. enabling them all to boost each other's xp gain, defense and initiative to silly levels. Making only one instance of each aura in an army count, would help to fix them a lot. In addition i'd say give them a penalty to xp gain compared to champions, and give them a longer recovery time after dying (10 turns?)

ohh number limits are a good idea too. perhaps a limit of 1-2 henchman for every champion you have, or one per each city, or every two cities.

in my last game i just made an unstoppable army of my soverign, a krax spearman i found, and five henchmen of differeing specialisations. by endgame they were all around lv32 and my army rating was long since past "epic"