Since there's a bit of a discussion of the most recent Supergirl reboot's character swings and roundabouts going on in the Casstoons post,
this seemed like a good time to post 3 pages of Superman/Batman annual 5 which address some of those issues.
A Reign of Doomsday tie-in, the basic setup is Sh*&, Meet Fan. Kara and Dick are trapped in the Watchtower with Doomsday and Cyborg Superman, who's turning the satellite into a giant weapon. Kara has apparently gotten hit with synthetic magic energy and is too ill to fight, so Dick gets her to sickbay, which he explains the JLA somehow turned into a "panic room" - it's cut off from all other systems, Cy.Sup can't reach it to manipulate it, and it's shielded from magic energy. Kara's well while she's in there, but only while she's in there. Dick leaves her to fight the Gruesome Twosome by his lonesome, and Kara accidentally triggers a full-body diagnostic scanner, which informs her she's dying. dun dun DUNNNN!
Through comms she passes word on to Dick, who in mid-battle tells her how to initiate sickbay's holographic Dr. Mid-Nite AI. Holo!Pieter confirms she's dying but can find no organic cause. So, Dick suggests one more option - the holographic Dr. Fate AI.( Your life is in your own hands. )
She does as he prescribes, and rejoins the battle. And then things get exponentially worse, but that's a tale for another post.