So why couldn't she revive him after he was shot through the chest?
Ichigo was on the brink of death, she rejected his wounds while he was barely alive, Orihime's power allows her to heal anyone as long as they have even the slightest bit of life.
If she had the power to revive the dead don't you think she'd be getting used a lot more for example Soul Society would have had her revive Yamamoto's Lieutenant and many others that had fallen.
Her powers have a limit, after all she's only human and to have her suddenly gain some major potential this far on in the series would feel rushed.
I get where you're coming from though Orihime's power has always been...debated personally I believe it is a fullbring but Kubo has never really confirmed what they are however other than healing and providing pretty weak shields there not that powerful nor do I see a potential where they could be powerful to make her that much of a threat.
at bold: She isn't there to revive them she was and is still in Hueco Mundo. They didn't know they'd get invaded or that any let alone that many would have died. Also some characters need to die to advance plot or for emotional responses from other characters, the main character however will never die.
As far as her powers, according to the manga according to Aizen, her powers along with Chads are a result of the Hogyoku responding to them by way of Ichigo. And she has the power to reject phenomena by denying or undoing events in various forms, meaning if she chooses to deny or not accept someones death she
could bring them back. Her skill Sōten Kisshun created an arm for Grimmjow out of nothing. And she can revive the dead check Bleach manga; Chapter 274, page 12 or 14 depending on the site and art pre-story on the site, But she revives L.oly(or one of those two jealous girls that gave her a hard time)
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Weak Shields? You mean the shield that stood up to the Sweeper at it's weakest and an attack from Ulquiorra at it's current best? Seems like a fairly reliable shield to me.
Also Chad's power was stated to be like that of a Hollow when they invaded Hueco Mundo and he showed an arm blast similar to a cero.
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Notice how his shield at "true" power looks like a face or hollow mask. Also Fullbringer's use a Hollow type Reiatsu
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As for whether he was dead or not I guess that's up to the manga, as I said his eyes flatten, he was stabbed in the heart(you can tell by the wound location), and he hasn't moved or breathed(his chest hasn't expanded and contracted) for 2 episodes, his body is completely limp when Grimmjow kicks him. Also you'll notice when she heals him here she says" This spiritual pressure around his wound...I can't reject it...Who did this" yet Ichigo revives and the shine returns to his eyes.
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I thinki the reason the Hollow "needed" to save Ichigo the second time was A) plot development B) Ulquiorra's ressurection Reiatsu was stronger than his generic reiatsu which was already hard for Orihime to reject, thus making the second wound twice as difficult.