When being stared at, Endermen will not attack the player if he/she is staring at the Enderman over 5 blocks above or below the Y-axis of the Enderman, regardless of how long they stare. This is very similar to the Ghast issue, MC-49640, and it is most probably because of this issue with the new pathfinding AI of all mobs.
Confirmed this is still happening as at 1.8.8