I finally worked this one out! It looks like it had to do with a formatting error in the Aarne-Thomspon list: of of the links had too many "s in a row, which made the HTML throw up its hands and give up in certain situations.

The Aarne-Thompson list should generate cards with all of its values, now, and when it's combined with other lists, it should also pull values from them. (It'll likely still be heavily weighted toward the Aarne-Thompson list, just because that list is so long, but I tested it by selecting every single pre-loaded list in the generator, and that gave me a card that was less than half Aarne-Thompson. Which is probably a testament to ysabetwordsmith's list-writing skills.)

Thanks again for bringing this to my attention, and for bearing with me. :) Let me know if you see any more weird behavior!