Canadiangunslinger has it right. The 5.56mm round was designed to be an assault rifle round, effective to around 250-300m. Beyond that range (and less than that from short barrelled carbines), it lacks sufficient velocity to fragment.
Note that it is not the yawing tumbling by itself, all spitzer shaped rifle bullets do that. The increased lethality occurs because it yaws sooner than larger/slower bullets, and at high velocity, the jacket is not strong enough to withstand the stresses imposed on it, so it fragments.
Usually it breaks apart at the canelure(sp?). The base and tip flatten out, shedding bits of jacket and lead fragments. The multiple wound tracks of these fragments sometimes join up when these tears elongate under cavitation. There is a velocity threshold below which this fragmentation and cavitation tearing no longer takes place.
Contrary to poular mythology, rifling pitch/twist rate has very little to do with it. The SS109/M855 is a little heavier, and thus has more mass to fragment and is just as, if not more lethal than the old M-193.
Part of the problem is that we now add optics to everything, including the C-9, which allows us to make hits at longer range than the cartidge is really designed for. Also, hit placement counts for a lot. No bullet is a magic death ray. Unless sufficient damage is done to the CNS, the only real wounding mechanism that counts is rapid blood loss and shock. If nothing vital is hit, any cartridge/bullet combo can fail. There were stories in the Falklands of multiple hits with 7.62 NATO not dropping the target instantly.
