That a time-inverted process doesn't contradict the fundamental laws doesn't mean that we could observe it with frequency basically comparable to that of the uninverted process. Think of thermodynamical irreversibility, for an example of class of processes which practically don't have inverted counterparts, even if these are perfectly compatible with microscopic physics.

Also, losing mass is not clearly defined process. If by mass of a BH one means the mass included below the horizon (or calculated from the diameter of the horizon) observed from constant distance, then black holes never lose or gain mass, since such an observer would never see anything cross the horizon in any direction: for an outside observer it takes infinite time for any falling object to reach the horizon.

If mass is calculated from the gravitational force measured in a constant distance, it may grow as mass gets attracted towards the horizon, or it may shrink if the mass near the horizon has enough outward momentum to overcome the gravity of the black hole. The latter scenario is quite unlikely to happen during typical black hole formation, at least I think so.