The several hours it takes to complete the resection of a brain aneurysm?
This is difficult to answer because you are essentially asking about the criteria for brain death. These are ever evolving with the discovery of new ways to image brain function and also these criteria are not yet uniform in all countries.
https://en.wikipedia.org/wiki/Brain_death
Having said that, I would say that the longest duration of a “flat line” EEG to recovery of full consciousness would be what now occurs almost routinely in many Neurosurgical wards when they perform resection of aneurysms, such as in the link below. Typically, the patient is hooked to a heart-lung machine and is technically “dead”, having no effective electrical activity in the heart. The brain is drained of blood and the EEG is “flat”, that is, the patient is brain dead. The body is cooled significantly to lower metabolism. The patient cited below happened to have a near-death experience, but that is beside the point. The point is that, after this type of surgery which can take hours to finish (3 to 8 hours), a formerly “brain dead” patient can recover and hopefully without cognitive impairment.
http://www.iands.org/research/important_studies/dr._pim_van_lommel_m.d._continuity_of_consciousness_5.html
Also, there is a distinction between brain death and somatic death, as illustrated in the link below. A pregnant woman who suffered brain death was kept alive to allow fetal maturation and better the chances of fetal survival.
There have been cases of demonstrated EEG activity for several hours (range of 2 to 168 hours, with a mean of 36.6 hours) after the diagnosis of brain death. However note that in this study, none of the patients recovered despite the demonstration of EEG activity.
Finally, EEG alone does not define brain death. Currently, and things may yet be refined as they always are in medicine, the most sensitive and accurate diagnosis of brain death is with the use of angiographic studies of the brain. To date, the definitive diagnosis of brain death is with the demonstration of absent intracerebral blood flow (by angiography).
http://www.neurotransmitter.net/braindeath.html
In short, the absence of brain wave activity does not necessarily mean brain death, or even simply “death”. This state can be artificially reproduced in brain surgery lasting several hours with patient recovery in the end. On the other hand, EEG activity can persist for days beyond the diagnosis of “brain death” using the UDDA (Uniform Diagnosis of Death Act) criteria. Finally, the EEG is the not the definitive tool for diagnosing brain death.