Kant's argument is that, while the soul may not be a collection of parts extended in space (therefore, not an extended quantity), it still has intensive quantity and, like a sound, it can gradually lose more and more existence until it fades out of existence altogether.

Is Kant's objection sound? We don't think so. As Roderick Chisholm points out:

(Kant) thought that some things could have more existence than others. It is as though he thought that there is a path between being and nonbeing, so that one day you may set out from nonbeing and head in the direction toward being with the result that the farther you go in that direction the more being you will have. But surely there is no mean between being and nonbeing. If something is on a certain path, then that something is. Or if it isn't yet, then it can't be on the path between being and nonbeing. Of course things can be more or less endowed. But a thing cannot be more or less endowed with respect to being. What is poorly endowed is poorly endowed and, therefore, is.

In cases like a sound gradually fading away or a mind gradually losing consciousness or some other faculties, what is really going on is the alteration of something that exists, not its gradually ceasing to be. Something can gradually be altered in the properties it possesses you can gradually lose your hearing but something cannot be gradually altered with respect to existence. That is all or nothing.