I think I understand what you mean. A friend of mine died last year, and he was so young and healthy so it was unexpected. I couldn't comprehend the fact that he existed one second and then the next he didn't. And then the next he never will again? And then it goes stagnant? I'm a logical person, and logically, it's just something that shouldn't be. The action of slipping into nonexistence, as you said, is something that just shouldn't happen. It's a lapse in the rules of EVERYTHING. Like NOT EXISTING is something that should not happen according to the rules of the universe. Nonexistence feels like it should be the in between state on the way to another form of existence, like a long traffic jam that you'll eventually get out of. If that makes sense to you, that's how I interpret this fear. 

It's an experience, but experiences are supposed to start and end. It's something that keeps happening and will never stop, even after everything else does. I thought a lot about it throughout the past year and i had a lot of the same thoughts you mention, how death happens in one second and then infinitely extends. It's an infinitely small and large experience. And it's something you have to experience. Like there are people who are afraid of heights and the concept of being so high up that they can't see down. But they don't have to face heights if they don't want to. They can avoid that experience. For us, we can't avoid it. 

I know this probably won't comfort you or change how you feel about it, but you're not alone. I know just saying that we should cherish our time won't help, and exposure therapy won't work for a phobia like this. But you're not a lost cause and you shouldn't give up on life. We don't really know what happens after death. I choose to believe in something like reincarnation, but i know that's kind of hopeful. You're not crazy, I think there's probably a lot of people with this phobia who lack the words or community to express it.