How does oxygen deprivation affect neural activity? It is increasingly common for someone to regain a heartbeat after a cardiac arrest. During the time that the person is without a heartbeat, and so without circulation, the brain is deprived of oxygen.
Why are there long-term consequences to temporary deprivation of oxygen?
I understand that the short-term effect of loss of oxygen to the brain is to make it impossible for the cell to maintain the gradients of ions needed to initiate action potentials. As long as the cells don't die, or not too many die, why is there often long-term neurologic damage after a heart attack.
My question differs to the question of what happens during a stroke. During a stroke the deprivation is longer and more focussed.
A stroke results in impaired blood flow. A lack of blood supply to the brain results in prolonged cortical hypoxia, cells die. Neuronal cells have a relatively high background metabolism, for example because of their reliance on ion pumping that costs energy. A lack of oxygen can kill a cell and therefore deplete the brain of thousands and thousands of neurons after a serious stroke. Depletion of certain areas of the brain of cells will reduce the output to other areas, and decrease the input to that area. Moreover, epileptic foci may appear, resulting in epileptic discharges in the brain, referred to as post-stroke seizures. 

Upon recovery, gross rearrangements may occur in the brain, alongside gross changes in cellular activities throughout the affected areas, due to the brain's plasticity.

Having said that, if the oxygen depletion is short, I don't see any reason why there should be gross changes in neuronal behavior after recovery.