Can it be possible to keep a permanent stream of consciousness even while sleeping?
For example, to a buddhist monk doing Vipassana, the best thing would be to get mindfull ALL the day. Can be that possible?
It is said that Buddha didnt really sleep, for instance.
It is possible to remain aware while being asleep. This tends to happen during meditation retreats where you're engaged in full-time meditation. Though when you go back to ordinary life it wears off.
In Dzogchen, and I can speak according to my understanding of hows ChNN teaches it, this can be solved when after the recognition of instant presence (not mere awareness) one gradually trains to integrate every action into practice, meaning one never abandons that state not mattering what one is doing. This aspect of the practice is one of the things that was most compelling in my decision to learn Dzogchen, exactly because the effects of intensive practice done while in retreat tend to wear off when one re engages in everyday activities. I think this point is very important for those who can't spend some years practicing in retreat conditions.