In this case I follow Lucretius' argument in book one, (1-551) which is if I recall correctly is largely that if matter were infinitely divisible then the universe as a whole would have long since disappeared.
As I see it the fact that a particular theory "works in practice" does not mean that it does not work for some reason outside the theory. And in this case there has obviously been no one who has demonstrated in the real world that matter can be "infinitely" divided.