I contacted SE support for this, but they just said to post here.

http://ffxiv.gamerescape.com/wiki/Tataru


That page says near the bottom "After you start the quest Coming to Ishgard, you can no longer challenge her at the Intercessory. You must complete all of the 3.0 storyline, which ends in the quest Heavensward, before you may challenge her again.

Once you complete the 3.0 Main Scenario questline, you may challenge her at The Forgotten Knight. Her deck changes and she is only able to be challenged between the hours of 7:00pm and 7:00am (Eorzean Time). Once you start the 3.1 Main Scenario via the An Uncertain Future quest, you lose the ability to challenge her at Triple Triad forever."

I'm right in that zone after finishing Heavensward, but did not start Uncertain Future. She is never in the Forgotten Knight and just stays in the Manor in the Pillars. No matter what time I try to talk to her there, no option comes up to challenge her.