Do you mean to say we 'die' each time we are unconscious? - alechol..
Obviously not.
Anaesthetic disrupts activity of the brain by producing changes in the brainstem and cerebral cortex. As a result we lose consciousness and have absolutely no memory - occasional mistakes by anaesthesiologists notwithstanding - of the time we were 'under'.
If reversible and temporary chemical changes to the brain destroys all consciousness how can consciousness possibly survive the complete destruction of our brains?
We are our brains.