During two Enderman kills that resulted in the spawning of an Endermite, the Endermite was unkillable with weapons or dropping sand/gravel on them. In the screen shot provided, that little guy spawned on the cobblestone stair spinning. I removed the stair and he stayed there in mid-air spinning. Tried to replace the stair and it acted like there was an entity in the way, not allowing the placement. The first time and Endermite spawned and was unkillable, it eventually (after several game days) despawned.