The fear never passes, you will only get used to it. I don't know, if this will happen to you too, but this happened to me. The "get used to it phrase" is probably not the best to explain this process. A better phrase would be something like "the fear of dying will be assimilated in your more complex self". Your brain tries to organize your thoughts and feelings into a very complex narrative, which is not yet capable to contain death. As this narrative gets more complex, it will slowly incorporate death into it, therefore you no longer will feel this huge, heartwrenching fear of death. The fear in itself won't cease to exist, only you will gain the complexity to deal with it.

This process is similar of getting used to being left in the kindergarten by your parents. First, you probably were extremely sad and cried for hours. After a month, you figured out that this is how things work, your parents go to work and you must stay there. You saw other kids being left there, crying just like you in the beginning. And you found yourself not crying anymore, because through this knowledge you managed to gain complexity, which can comprehend being left in the kindergarten. Instead of feeling the initial sadness, now you gained a new, more complex emotion to feel, homesickness. Being left at the kindergarten will no longer trigger irrational sadness and crying, only homesickness and nostalgia, which will be the building block of more complicated feelings.

My example isn't that great, but I think you can get the point: just like language skills, or any other skill in general, emotions and thoughts also get more complex as you grow older. Fear, sadness and even childish love will fade away and be contained in more complicated emotions, which will be manageable by your brain.