Oh, I see now! I'm not a mathematician, therefore, I can't grasp the concept fully. First of all, it does not need to become zero for the problem to exist. Secondly, the key point is "approach zero".
It might sound condescending. But it's not. It is really a concept that is hard for non-mathematicians to understand, because people rarely get to think about infinite things.
See, you still haven't understood it: The number of active bitcoins will NOT "approach zero". Not at all. It will approach some large positive number. Ofcourse, it is hard so estimate the exact number today, but I believe it will be more than half the number of total bitcoins, that is more than 10.5 million.