Quick thought experiment: two particle-antiparticle pairs get created:
p1-ap1, p2-ap2
In regular space, after a very short amount of time p1 annihilates with ap1 and p2 with ap2. Net result is zero additional matter and energy, otherwise we'd just be creating random matter and/or energy everywhere.
If the same happens at the event horizon of a black hole and let's assume purely by chance, p1 and ap2 fall in and p2 and ap1 do not. After a short while, p1 and ap2 annihilate inside and p2 and ap1 outside. The result should be effectively the same as in the previous case, thus zero net energy and/or matter on either side. Thus, also no radiation and mass loss.
It'd be nice if an actual physicist chimed in at this point and told me where I went wrong :)