I haven't found any hard caps, but in my experience, ATH has the most modest gains of any skillset. I'd have to check to be sure, but I don't think I've ever seen ATH break 40 points of improvement. Usually, even high-high ATH has improvement between 27 and 35.
SPD I've definitely seen break 40, but I don't recall seeing it break 45.
DEF is more like SPD. I know I've seen it hit 45, but I can't think off the top of my head of a guy who broke 45 points of DEF improvement.