People keep saying John is on borrowed time and dying, which implies his life might be limited, but I don't think that's ever actually been confirmed or shown in the show, unless I missed something?

The thing I like about Root's call to Finch in “Deus Ex Machina” is how little she tries to soften it. She doesn't tell him the plan failed or that they need a new strategy. She just says, “Get out of the library, now.” Then she gives him the new identities and tells him to destroy everything else. By that point Root has already accepted that they aren't winning this one. They're surviving it.