Most likely this character is only meant to support you in combat. If he survives, he just tells us to move forward, being very tired after combat.
If you like to have him alive, you can dispose all of the small mobs around Junzou without talking to Nogami (this is fairly easy by de-aggroing), use stealth hit on Junzou to remove one health bar, and then run and talk to Nogami to initiate him into combat. Or do not talk to him at all. This will trigger alternative sequence - he will rush to combat already after fight is finished, and will comment, that area is apparently clear.
Update: After progressing story further, I can tell, that saving him doesn't matter a lot. Medium spoilers ahead:
Doing certain choices, you gain possibility to visit Hirata Estate a little bit after you were there for the first time, which gives you some additional insight on what happened there. And on the same place of fight with Junzou the Drunkard, you find corpse of Nogami Gensai even if you saved him before. Which means, he ultimately dies anyway. You can find handful of ash on his corpse, I'm not sure if it is different if you don't save him.