Of course, 4e had a mechancially elegant solution to this - Reaping Strike is just one of several powers the fighter will have, including encounter powers that s/he will use from time to time, and so there will be occasions when the fighter misses.If an attack is competent enough to deal hit point damage to a defender, it should not be described as a "miss". It translates to "this reaper guy always deals damage", which completely tramples over my believability meter as no one should absolutely always hit.
Another solution to the problem is a narrative one - some of those "hits" that are not fatal can be narrated, in the fiction, as misses ("You swing your axe, almost cleaving your foe's skull in two - but at the last minute he rolls out of the way, and your axeblade leaves a deep groove in the timber floor.") No physical injury is dealt, but luck/divine favour etc are depleted.
I wouldn't expect this narrative treatment to satisfy those who don't like Reaper - the point of putting it forward, rather, is to try to show that there is no default narrative (such as "this guy never misses") that Reaper brings with it. Rather, it depends upon whether or not the mechanics of the game (attack rolls, hits and misses, hit point depletion, etc) are seen as process simulation or not.