Imagine that you are a super intelligent alien, and what you are experiencing right now as "your life" is a vivid dream. When you wake up, you will remain conscious, but you won't be the you that you were in the dream in any appreciable way.
This is roughly analagous to the way many theologians who are literate in the philosophy of mind talk about life after death. You have a transcendent consciousness that is intertwined with the brain throughout mortality, but that cannot be reduced to the brain. Upon death, this consciousness is liberated from the physical world.
I’m not saying I believe that, but theologians MUCH smarter than me and than most of the people who post here have spent entire careers thinking about what a post-mortal existence could be like. They are not stupid, or deluded, or engaged in an exercise in wishful thinking. If you want to sample how they think in a format suitable for an educated lay reader, you can pick up something like this:
Anyone who wants to dismiss Hart's ideas out of hand should do so in their own book published by Yale University Press or its equivalent. Simply put, the existence of consciousness poses problems for materialist philosophers. I'm not saying "therefore God." I'm just responding in the affirmative to the original question posed by the OP: i.e., can a reasonable person believe that consciousness can persist after the body dies? Yes. Many reasonable people believe this.
Like everyone else, I have no clue what happens after death. Most probably this life is all there is. But one of the things that makes this subreddit a drag (and I’m not talking about you here …) is that some of the cocksure atheists who troll around in here think that all believers adhere to some sort of hillbilly, cornpone fundamentalism, and they think they’re scoring points when they point out the limitations of this kind of theology. I think atheism is a completely reasonable and defensible position. I flirt with it myself. But many of the theists in here who haven’t thrown up their hands and left are also quite reasonable. It is wearisome to see an educated, informed commenter get downvoted into oblivion because some kid who just finished reading The God Delusion thinks he's a warrior for rational thought.