I don't think the fear of not-being is rational. I don't think it's rational either but sometimes people can't help having non-rational fears.

You can't fear something you will never experience maybe it's more about being afraid of the unknown , of the possible emptiness after life.(I'm not a theist )
if you really end up not being, there will be no you to experience the not being.Yes,when the times come for not being you won't , but you're aware of it now, and that's frightening.

I have no idea what 's on the menu once dead, I just know that I don't know and I live in hope that there's something .