IMO, the most likely unintentional failure mode for a carrier would be the gas rings wearing the ID enough that gas leaks around the rings and causes short stroking or bolt lock up issues due to the lug misalignment. This would require at least several sets of gas rings and would probably be 75k-100k rounds or more before the effect became significant enough to notice or warrant action.
Otherwise, if you were running the rifle significantly over gassed, the rear of the cam groove could get deformed/cracked due to the energy it absorbs from the cam impact (energy that's not absorbed by the recoil spring). Steel has an infinite fatigue life below which the load will never cause failure. So, you would have to be doing something seriously wrong to cause this much stress in the cam groove and the gas key would probably break before the BCG sustained damage.
Or, if you intentionally ran very fine dust/sand in the weapon, something like talcum powder sized but abrasive like sand, this would be along the lines of an industrial dirt wear test. Eventually the carrier would wear down the rails in the upper to a point where it may not align with the RE when in battery and this would prevent lockup or induce cycling problems. Again, this would have to be intentional abuse since we're talking running moon dust in the rifle and not cleaning it, and it would take many many rounds for it to happen. Never heard of this happening in either Sandbox (Iraq or A-stan), so---
No, your BCG will probably outlive you unless you break it on purpose.