Description says persuasion attempts almost always succeed and that the amulet enhances Speechcraft 35%, where UESP says it works all the time, and the % can vary. Neither mention the effect it has on Intimidate options.

I just attempted to intimidate the bandit at Valtheim Towers, an I am wear the AoA, Speechcraft 100, and the Intimidate perk. I failed the attempt. Is that just an impossible attempt? No other way I could have failed it, right? Or does the amulet not effect intimidate checks at all?

Some intimidate checks are scripted to fail...like the thief that tries to mug you...he always resists your intimidation.

I too have never made the intimidate check at Valthaim Towers.