Sometimes he disappears (not sure if he runs away) but mostly he goes down into a "bleed out" state.
I was planning a few hacky solutions, but since I have a save right before this, and other things I could be doing, I'll hold off and see if 1.0.9 fixes the issue.
The issue seems simple, that Jake only has a couple hit points — much like Grelod the Kind in Skyrim, in the Riften orphanage — and will go down in one hit, any kind of hit. If you're gonna throw literally dozens of Gunners at the Sole Survivor, Jake should either, A, be able to defend himself, or, if that's not in his character, B, run for cover. Like, when Aiden fires, Jake should high-tail it for cover in the existing buildings. This would actually be ideal as it would give the player direction, since, without cheating, the fight is extremely difficult even on Normal if you don't do that.
But, I'm not a developer, I don't know a lot about what's going on behind the scenes... Much appreciated if you can fix it.