I think that it is a tie for me, between finally, FINALLY, getting the August Celestials Cloud Serpent, and Over Their Heads, from the Klaxxi Daily Quest "Dark Skies."
For the latter, I made sure that I didn't kill more than one or two of the mobs per run, and I didn't target any of the larger targets. I ran this for 59 straight days, but two of the listed targets (Amber-Shaper Un'sok and Dread Ambercrusher) just did NOT show up. Everything else appeared, day after day, ad nauseum, but not these two NPCs.
After smacking my head against this wall, I finally began writing tickets to Blizzard, asking if there might be a problem with the way that the NPCs showed up for this particular Daily. I received no reply, which is practically a given, but I did get Un'sok the day after the first ticket. It was another two weeks before the Dread Ambercrusher finally put in an appearance, with six more tickets being sent in to Blizzard.