Have people been resuscitated after say, 30 mins or even an hour, and managed to have their brain functions relatively intact?
Absolutely. Look up "Mammalian Diving Reflex".
Brain damage from short-term clinical death happens primarily after revival. The valves routing blood to the parts of the brain that need it stick in the state they were in when the oxygen finally failed.
Muscles contract with stored energy and require metabolism to relax. "Valve off" is contracted, so when blood flow and oxygen is restored, the valves for regions of the brain that were turned down don't get oxygen and can't reopen - and without the blood flow they can't get oxygen, in a viscous circle. Raising the blood pressure to try to force them just blows the vessels, causing a stroke. The
nerves die over a half hour to an hour (and kill each other off through glutamate cascade, as dying nerves release glutamate that causes others to fire, deplete their remaining energy reserves, and die in turn.
Mammals, though, have a reflex related to deep diving. When diving deep, the increased pressure increases the partial pressure of oxygen, keeping things running until most of the oxygen is used up. Then coming back back up lowers the pressure further and can leaver the brain oxygen starved for long enough to produce the "valves stuck" phenomenon. To prevent this, mammals have the following reflex: When oxygen is running out AND the body (I think it's the back of the neck) is cold, the valves all open up, so any that get stuck are in the open position. Once oxygen is restored the blood flows, the nerves survive, the muscle gets repowered, and all is well - if thing hadn't been shut down long enough that too many cells died meanwhile.
This was discovered when some victims of drowning in cold water recovered just fine, with no brain damage, after half an hour or more of clinical death. I think the time before damage sets in is something between 25 and 45 minutes.
I don't know how CI's current protocols work. But ALCOR's are designed to include activating the diving reflex, if possible, so the brain's valves stick in the open position.
(This is more to encourage better perfusion of cryoprotectants than to try to make the brain restartable: As of the last time I looked the thought was that brains preserved - even by the best techniques available at the time - would require rebuilding by nanotechnology, so the idea was to preserve as much as possible of whatever might encode memory and personality.)