Is spiritual awakening a continuous process or a one time event?
It is a process, yes, but it doesn’t mean it’s infinite and there is no point after which there are no more “spiritual” realizations. The beginning of this process (awakening or self-realization) is usually intense and dramatic, the end of this process (enlightenment) is very quiet and almost unnoticeable. There is absolutely no spirituality at the end of this process. Spirituality is a vehicle to deliver you home, it’s not home. Once you take the trip, the vehicle is abandoned.
People who say it’s a continuous process, it’s an infinite journey and alike are, in reality, usually still dreaming. They had a glimpse of their infinity, but they haven’t collapsed into it yet. Their egos interpret it as an “infinite path”. The path is not infinite - the path itself is an illusion. Sometimes they still harbor extraordinary beliefs, for example, beliefs in future lives and reincarnation. What hides behind these beliefs is the desire to live forever, the desire for infinite existence, which is coming from the fear of non-existence. This desire is an egoic desire. You cannot know non-existence while you still cling to existence. In Buddhism, they say Buddhas are free from desire of both material and non-material existence, which is meant to say, both in form or as a formless soul.
Based on your question, I take it you’re one of those people? ;)
You may be eternal, but your life is not infinite. There will be no future lives. Accept that, don’t run away from it.